A073376 Sixth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

1, 7, 42, 196, 826, 3150, 11256, 38004, 122787, 381997, 1151458, 3376968, 9671284, 27123292, 74669472, 202181112, 539342181, 1419492627, 3690464106, 9487902396, 24143758254, 60861096714

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,-49,91,161,-357,-363,714,644,-728,-784,224, 448,128).

Formula

a(n) = Sum_{k=0..n} b(k) * c(n-k), with b(k) = A001045(k+1) and c(k) = A073375(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+6, 6) * binomial(n-k, k) * 2^k.

a(n) = ((1+n)*(4884880 +4449396*n +1525272*n^2 +247653*n^3 +19152*n^4 +567*n^5)* U(n+1) + 2*(2+n)*(2321720 +2182242*n +765993*n^2 +126621*n^3 +9927*n^4 +297*n^5 )*U(n))/(6!*3^9) with U(n) = A001045(n+1), n>=0.

G.f.: 1/(1-(1+2*x)*x)^7 = 1/((1+x)*(1-2*x))^7.

E.g.f.: (1/(6!*3^10))*( 4096*(9305 +56535*x +83745*x^2 +47700*x^3 +12060*x^4 +1350*x^5 +54*x^6)*exp(2*x) + (4402000 -5784960*x +2454120*x^2 -457920*x^3 +41130*x^4 -1728*x^5 +27*x^6)*exp(-x)). - G. C. Greubel, Sep 29 2022

Mathematica

Table[(2^(n+7)*(297760 +500640*n +302778*n^2 +87255*n^3 +12915*n^4 +945*n^5 +27*n^6) +(-1)^n*(4402000 +4038132*n +1453788*n^2 +265545*n^3 +26145*n^4 +1323*n^5 +27*n^6))/(6!*3^10), {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^7 )); // G. C. Greubel, Sep 29 2022
(SageMath)
def A073376(n): return (2^(n+7)*(297760 +500640*n +302778*n^2 +87255*n^3 +12915*n^4 +945*n^5 +27*n^6) +(-1)^n*(4402000 +4038132*n +1453788*n^2 +265545*n^3 +26145*n^4 +1323*n^5 +27*n^6))/(factorial(6)*3^10)
[A073376(n) for n in range(40)] # G. C. Greubel, Sep 29 2022

Crossrefs

Seventh (m=6) column of triangle A073370.

Cf. A001045, A073375.

Sequence in context: A008526 A057425 A248329 * A094429 A246434 A255614

Adjacent sequences: A073373 A073374 A073375 * A073377 A073378 A073379

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved