A118353 Semi-diagonal (two rows below central terms) of pendular triangle A118350 and equal to the self-convolution cube of the central terms (A118351).

1, 3, 21, 163, 1353, 11760, 105681, 973953, 9154821, 87428388, 845894700, 8273978100, 81682757317, 812829371205, 8144563709391, 82104333340467, 832125695906313, 8473862660311392, 86661931504395228, 889705959333345756

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Mathematica

T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==n, 0, T[n-1, k] - 3*T[n-1, k-1] + 3*T[n, k-1] + T[n+1, k-1] ]];
Table[T[n, n-3], {n, 3, 30}] (* G. C. Greubel, Feb 18 2021 *)

Prog

(PARI) my(x='x+O('x^33)); Vec((serreverse(x*(1-3*x+sqrt((1-3*x)*(1-7*x)))/2/(1-3*x))/x)^3)
(Sage)
@CachedFunction
def T(n, k):
    if (k<0 or n<k): return 0
    elif (k==0): return 1
    elif (k==n): return 0
    else: return T(n-1, k) - 3*T(n-1, k-1) + 3*T(n, k-1) + T(n+1, k-1)
[T(n, n-3) for n in (3..30)] # G. C. Greubel, Feb 18 2021

Crossrefs

Cf. A118350, A118351, A118352, A118354.

Sequence in context: A166696 A058194 A179815 * A365132 A371817 A262977

Adjacent sequences: A118350 A118351 A118352 * A118354 A118355 A118356

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2006

Status

approved