|
Search: chatham
|
|
|
| A103330 |
|
Number of ways to place n+1 queens and a pawn on an n X n board so that no two queens attack each other. |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 16, 20, 128, 396, 2288, 11152, 65712, 437848, 3118664, 23387448, 183463680, 1474699536
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
R. D. Chatham, G. H. Fricke and R. D. Skaggs, The Queens Separation Problem, Utilitas Mathematica 69 (2006), 129-141.
|
|
EXAMPLE
|
a(4) = 0 because when 5 queens are placed on a 4 X 4 board, at least 2 queens will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A000170 A103331.
Sequence in context: A104010 A102544 A152022 this_sequence A045667 A045658 A167305
Adjacent sequences: A103327 A103328 A103329 this_sequence A103331 A103332 A103333
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Jan 31 2005
|
|
EXTENSIONS
|
Further terms from R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Feb 15 2005, Apr 20 2007, Apr 28 2007
a(12) corrected by R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), May 12 2009
|
|
|
|
|
| A103331 |
|
Number of ways to place n+1 queens and a pawn on an n X n board so that no two queens attack each other (symmetric solutions count only once). |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 2, 3, 16, 52, 286, 1403, 8214, 54756, 389833, 2923757, 22932960, 184339572
(list; graph; listen)
|
|
|
OFFSET
|
1,6
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, G. H. Fricke and R. D. Skaggs, The Queens Separation Problem, Utilitas Mathematica 69 (2006), 129-141.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Indepe ndence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
|
|
EXAMPLE
|
a(4) = 0 since when 5 queens are placed on a 4 X 4 board, at least two of them will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A103330, A002562.
Sequence in context: A012358 A012700 A012705 this_sequence A052506 A052858 A073997
Adjacent sequences: A103328 A103329 A103330 this_sequence A103332 A103333 A103334
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Jan 31 2005
|
|
EXTENSIONS
|
More terms from R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Feb 15 2005, Apr 20 2007
|
|
|
|
|
| A129551 |
|
Number of ways to place n+2 queens and 2 pawns on an n X n board so that no two queens attack each other. |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 0, 4, 44, 280, 1304, 12452, 105012, 977664, 9239816, 90776620, 897446092
(list; graph; listen)
|
|
|
OFFSET
|
1,7
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
|
|
EXAMPLE
|
a(4)=0 because when 6 queens are placed on a 4 X 4 board, at least two queens will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A000170, A129552.
Sequence in context: A051223 A077435 A074751 this_sequence A081078 A035014 A030987
Adjacent sequences: A129548 A129549 A129550 this_sequence A129552 A129553 A129554
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Apr 20 2007
|
|
|
|
|
| A129552 |
|
Number of ways to place n+2 queens and 2 pawns on an n X n board so that no two queens attack each other (symmetric solutions count only once). |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 0, 1, 6, 37, 164, 1572, 13133, 122279, 1155103, 11347863, 112182378
(list; graph; listen)
|
|
|
OFFSET
|
1,8
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
|
|
EXAMPLE
|
a(4)=0 because when 6 queens are placed on a 4 X 4 board, at least two queens will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A002562, A129551.
Sequence in context: A129651 A097297 A047670 this_sequence A056338 A056328 A156185
Adjacent sequences: A129549 A129550 A129551 this_sequence A129553 A129554 A129555
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Apr 20 2007
|
|
|
|
|
| A129553 |
|
Number of ways to place n+3 queens and 3 pawns on an n X n board so that no two queens attack each other. |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 0, 0, 8, 44, 528, 5976, 77896, 1052884, 13666360
(list; graph; listen)
|
|
|
OFFSET
|
1,8
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
|
|
EXAMPLE
|
a(4)=0 because when 7 queens are placed on a 4 X 4 board, at least two queens will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A000170, A129554.
Sequence in context: A112908 A001689 A028565 this_sequence A075863 A118838 A153828
Adjacent sequences: A129550 A129551 A129552 this_sequence A129554 A129555 A129556
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Apr 20 2007
|
|
|
|
|
| A129554 |
|
Number of ways to place n+3 queens and 3 pawns on an n X n board so that no two queens attack each other (symmetric solutions count only once). |
|
+10
2
|
|
| 0, 0, 0, 0, 0, 0, 0, 1, 6, 66, 751, 9737, 131672, 1708295
(list; graph; listen)
|
|
|
OFFSET
|
1,9
|
|
|
LINKS
|
R. D. Chatham, The N+k Queens Problem Page.
R. D. Chatham, M. Doyle, G. H. Fricke, J. Reitmann, R. D. Skaggs and M. Wolff, Independence and Domination Separation in Chessboard Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, to appear.
|
|
EXAMPLE
|
a(4)=0 because when 7 queens are placed on a 4 X 4 board, at least two queens will be adjacent and therefore mutually attacking.
|
|
CROSSREFS
|
Cf. A002562, A129553.
Sequence in context: A119232 A131519 A022024 this_sequence A165229 A127857 A127858
Adjacent sequences: A129551 A129552 A129553 this_sequence A129555 A129556 A129557
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
R. Douglas Chatham (d.chatham(AT)moreheadstate.edu), Apr 20 2007
|
|
|
Search completed in 0.031 seconds
|
