The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A119335 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A119335

Number triangle T(n,k) = Sum_{j=0..n-k} C(k,3j)*C(n-k,3j).
(history; published version)

#16 by Alois P. Heinz at Thu Sep 14 03:40:24 EDT 2023

STATUS

proposed

approved

#15 by Jean-François Alcover at Thu Sep 14 03:38:02 EDT 2023

STATUS

editing

proposed

#14 by Jean-François Alcover at Thu Sep 14 03:37:54 EDT 2023

MATHEMATICA

T[n_, k_] := Sum[Binomial[k, 3j] Binomial[n-k, 3j], {j, 0, n-k}];

Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Sep 14 2023 *)

STATUS

approved

editing

#13 by Alois P. Heinz at Tue Mar 12 08:08:53 EDT 2019

STATUS

proposed

approved

#12 by Seiichi Manyama at Tue Mar 12 07:57:01 EDT 2019

STATUS

editing

proposed

#11 by Seiichi Manyama at Tue Mar 12 07:54:38 EDT 2019

FORMULA

Column k has g.f. (x^k/(1-x)) *sum Sum_{j=0..k, } C(k,3j)(x/(1-x))^(3j)}.

#10 by Seiichi Manyama at Tue Mar 12 07:51:28 EDT 2019

NAME

Number triangle T(n,k) =sum Sum_{j=0..n-k, } C(k,3j)*C(n-k,3j)}.

#9 by Seiichi Manyama at Tue Mar 12 07:50:09 EDT 2019

LINKS

Seiichi Manyama, <a href="/A119335/b119335.txt">Table of n, a(n) for Rows n = 0..9869139, flattened</a>

#8 by Seiichi Manyama at Tue Mar 12 07:49:06 EDT 2019

LINKS

Seiichi Manyama, <a href="/A119335/b119335.txt">Table of n, a(n) for n = 0..9869</a>

#7 by Seiichi Manyama at Tue Mar 12 07:44:27 EDT 2019

EXTENSIONS

More terms from Seiichi Manyama, Mar 12 2019