A073374 Fourth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

1, 5, 25, 95, 340, 1106, 3430, 10130, 28915, 80035, 216143, 571225, 1482110, 3783640, 9522740, 23665300, 58149845, 141435985, 340854645, 814589475, 1931900376, 4549699950, 10645737330, 24761578470

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 (5,0,-30,15,81,-30,-120,0,80,32).

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073373(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+4, 4) * binomial(n-k, k) * 2^k.

a(n) = (5*(2968 +1974*n +411*n^2 +27*n^3)*(n+1)*U(n+1) + 2*(9412 +6099*n +1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) = A001045(n+1), n>=0.

G.f.: 1/(1-(1+2*x)*x)^5 = 1/((1+x)*(1-2*x))^5.

E.g.f.: (1/157464)*(512*(263 + 1104*x + 1026*x^2 + 306*x^3 + 27*x^4)*exp(2*x) + (22808 - 24432*x + 7344*x^2 - 792*x^3 + 27*x^4)*exp(-x)). - G. C. Greubel, Sep 29 2022

Mathematica

Table[(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)

Prog

(Magma) [(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464: n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073374(n): return (2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464
[A073374(n) for n in range(40)] # G. C. Greubel, Sep 29 2022

Crossrefs

Fifth (m=4) column of triangle A073370.

Cf. A001045, A073373.

Sequence in context: A228457 A213293 A203184 * A126878 A203340 A055343

Adjacent sequences: A073371 A073372 A073373 * A073375 A073376 A073377

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved