A073375 Fifth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

1, 6, 33, 140, 546, 1932, 6454, 20448, 62271, 183202, 523887, 1461516, 3991400, 10698072, 28203612, 73265056, 187822125, 475788222, 1192287117, 2958453036, 7274927646, 17741533668, 42937126290

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 (6,-3,-40,45,126,-141,-252,180,320,-48,-192,-64).

Formula

a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073374(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+5, 5) * binomial(n-k, k) * 2^k.

a(n) = (n+3)*(n+9)*((3080 +1086*n +93*n^2)*(n+1)*U(n+1) + 2*(1660 +591*n +51*n^2) *(n+2)*U(n))/(5!*3^7) with U(n) = A001045(n+1), n>=0.

G.f.: 1/(1-(1+2*x)*x)^6 = 1/((1+x)*(1-2*x))^6.

E.g.f.: (1/787320)*(1024*(675 +3470*x +4195*x^2 +1830*x^3 +315*x^4 +18*x^5 )*exp(2*x) + (96120 -115640*x +42440*x^2 -6360*x^3 +405*x^4 -9*x^5)*exp(-x)). - G. C. Greubel, Sep 29 2022

Mathematica

Table[(n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)

Prog

(Magma) [(n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320: n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073375(n): return (n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320
[A073375(n) for n in range(40)] # G. C. Greubel, Sep 29 2022

Crossrefs

Sixth (m=5) column of triangle A073370.

Cf. A001045, A073374.

Sequence in context: A082106 A297392 A263479 * A089097 A120009 A074087

Adjacent sequences: A073372 A073373 A073374 * A073376 A073377 A073378

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved