|
Search: id:A132439
|
|
|
| A132439 |
|
Square array a(m,n) read by antidiagonals, where a(m,n) is the number of ways to move a chess queen from the lower left corner to square (m,n), with the queen moving only up, right, or diagonally up-right. |
|
+0
2
|
|
| 1, 1, 1, 2, 3, 2, 4, 7, 7, 4, 8, 17, 22, 17, 8, 16, 40, 60, 60, 40, 16, 32, 92, 158, 188, 158, 92, 32, 64, 208, 401, 543, 543, 401, 208, 64, 128, 464, 990, 1498, 1712, 1498, 990, 464, 128, 256, 1024, 2392, 3985, 5079, 5079, 3985, 2392, 1024, 256
(list; graph; listen)
|
|
|
OFFSET
|
1,4
|
|
|
COMMENT
|
a(m,n) is the sum of all the entries above it plus the sum of all the entries to the left of it plus the sum of all the entries on the northwest diagonal from it.
|
|
FORMULA
|
a(1,1)=1;a(1,2)=1;a(1,3)=2;a(2,1)=1;a(2,2)=3;a(2,3)=7;a(3,1)=2;a(3,2)=7;a(3,3)=22;a(m,n) = 2*a(m-1,n)+2*a(m,n-1)-a(m-1,n-1)-3*a(m-2,n-1)-3*a(m-1,n-2)+4*a(m-2,n-2), where m >=3 or n >= 3 and a(m,n)=0 if m <= 0 or n <= 0; generating function = (xy-x^2y-xy^2+x^3y^2+x^2y^3-x^3y^3)/(1-2x-2y+xy+3x^2y+3xy^2-4x^2y^2).
|
|
EXAMPLE
|
The table begins
1 1 2 4 8 16 32 ...
1 3 7 17 40 92 208 ...
2 7 22 60 158 401 990 ...
4 17 60 188 543 1498 3985 ...
8 40 158 543 1712 5079 14430 ...
a(3,4)=4+17+2+7+22+1+7=60
|
|
CROSSREFS
|
Cf. A035002.
Sequence in context: A130542 A128502 A079159 this_sequence A116217 A108838 A105070
Adjacent sequences: A132436 A132437 A132438 this_sequence A132440 A132441 A132442
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Martin J. Erickson (erickson(AT)truman.edu), Nov 13 2007
|
|
|
Search completed in 0.002 seconds
|
