|
Search: id:A064191
|
|
|
| A064191 |
|
Triangle T(n,k) (n >= 0, 0 <= k <= n) generalizing Motzkin numbers. |
|
+0
2
|
|
| 1, 1, 1, 2, 1, 1, 4, 2, 2, 1, 9, 4, 5, 2, 1, 21, 9, 12, 5, 3, 1, 51, 21, 30, 12, 9, 3, 1, 127, 51, 76, 30, 25, 9, 4, 1, 323, 127, 196, 76, 69, 25, 14, 4, 1, 835, 323, 512, 196, 189, 69, 44, 14, 5, 1, 2188, 835, 1353, 512, 518, 189, 133, 44, 20, 5, 1, 5798, 2188, 3610, 1353
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
This triangle appears on page 9 of the linked reference and is defined by Corollary 2.4.
A number triangle with repeated columns of A064189. Production matrix is A070909 (without first term ). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 02 2009]
|
|
LINKS
|
J. L. Arregui, Tangent and Bernoulli numbers related to Motzkin and Catalan numbers by means of numerical triangles.
|
|
FORMULA
|
T(n, 0) = sum(T(n-1, k) : k = 0, ..., n-1). For k even, 0 < k <= n, T(n, k) = sum(T(n-1, j) : j = k-1, ..., n-1). For k odd, 0 < k <= n, T(n, k) = T(n-1, k-1). - David Wasserman (wasserma(AT)spawar.navy.mil), Jul 15 2002
|
|
EXAMPLE
|
1; 1,1; 2,1,1; 4,2,2,1; ...
|
|
CROSSREFS
|
First column gives A001006.
Sequence in context: A156861 A122773 A029268 this_sequence A127420 A129033 A054090
Adjacent sequences: A064188 A064189 A064190 this_sequence A064192 A064193 A064194
|
|
KEYWORD
|
nonn,tabl,easy,new
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Sep 21 2001
|
|
EXTENSIONS
|
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jul 15 2002
|
|
|
Search completed in 0.002 seconds
|
