|
Search: id:A118923
|
|
|
| A118923 |
|
Triangle T(n,k) built by placing T(n,1)=A000012(n) in the left edge, T(n,n)=A079978(n-1) on the right edge, and filling the body with the Pascal recurrence T(n,k) = T(n-1,k)+T(n-1,k-1). |
|
+0
1
|
|
| 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 1, 3, 3, 2, 0, 1, 4, 6, 5, 2, 0, 1, 5, 10, 11, 7, 2, 1, 1, 6, 15, 21, 18, 9, 3, 0, 1, 7, 21, 36, 39, 27, 12, 3, 0, 1, 8, 28, 57, 75, 66, 39, 15, 3, 1, 1, 9, 36, 85, 132, 141, 105, 54, 18, 4, 0, 1, 10, 45, 121, 217, 273, 246, 159, 72, 22, 4, 0, 1, 11, 55, 166
(list; table; graph; listen)
|
|
|
OFFSET
|
1,8
|
|
|
COMMENT
|
The fourth diagonal is 1 2 5 11 21 ... which is 1 + A000292. The fifth diagonal is 0,2,7,18,39,75,132,217,338,504,725,1012,... which is A051743.
The array A007318 is generated by placing A000012 on both edges with the same pascal-like recurrence, and the array A059259 uses edges defined by A000012 and A059841. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2008
|
|
EXAMPLE
|
The table begins
1
1 0
1 1 0
1 2 1 1
1 3 3 2 0
1 4 6 5 2 0
1 5 10 11 7 2 1
1 6 15 21 18 9 3 0
|
|
MAPLE
|
A000012 := proc(n) 1 ; end: A079978 := proc(n) if n mod 3 = 0 then 1; else 0 ; fi ; end: A118923 := proc(n, k) if k = 1 then A000012(n); elif k = n then A079978(n-1) ; else A118923(n-1, k)+A118923(n-1, k-1) ; fi ; end: for n from 1 to 15 do for k from 1 to n do printf("%d, ", A118923(n, k)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2008
|
|
CROSSREFS
|
Cf. A000292, A079978, A008620, A079998, A051743, A077947.
Sequence in context: A110541 A079115 A072906 this_sequence A047010 A047100 A124772
Adjacent sequences: A118920 A118921 A118922 this_sequence A118924 A118925 A118926
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Alford Arnold (Alford1940(AT)aol.com), May 05 2006
|
|
EXTENSIONS
|
Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 21 2008
|
|
|
Search completed in 0.004 seconds
|
