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A118353
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Semi-diagonal (two rows below central terms) of pendular triangle A118350 and equal to the self-convolution cube of the central terms (A118351).
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5
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1, 3, 21, 163, 1353, 11760, 105681, 973953, 9154821, 87428388, 845894700, 8273978100, 81682757317, 812829371205, 8144563709391, 82104333340467, 832125695906313, 8473862660311392, 86661931504395228, 889705959333345756
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history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..500
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A118350, A118351, A118352, A118354.
Sequence in context: A166696 A058194 A179815 * A262977 A214391 A046637
Adjacent sequences: A118350 A118351 A118352 * A118354 A118355 A118356
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KEYWORD
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nonn,changed
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AUTHOR
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Paul D. Hanna, Apr 26 2006
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STATUS
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approved
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