A073373 Third convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

1, 4, 18, 60, 195, 576, 1644, 4488, 11925, 30860, 78278, 195012, 478599, 1159080, 2774880, 6575280, 15439065, 35955540, 83118970, 190862860, 435601611, 988620624, 2232236628, 5016441240, 11224087965

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 (4,2,-20,-1,40,8,-32,-16).

Formula

a(n) = Sum_{k=0..n} b(k) * c(n-k), with b(k) = A001045(k+1) and c(k) = A073372(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+3, 3) * binomial(n-k, k) * 2^k.

a(n) = ((350+177*n+21*n^2)*(n+1)*U(n+1) + 2*(277+132*n+15*n^2)*(n+2)*U(n))/ (2*9^3) with U(n) = A001045(n+1), n>=0.

G.f.: 1/(1-(1+2*x)*x)^4 = 1/ ( (1+x)^4*(1-2*x)^4 ).

E.g.f.: (1/4374)*(32*(113 + 366*x + 234*x^2 + 36*x^3)*exp(2*x) - (-758 + 690*x - 153*x^2 + 9*x^3)*exp(-x)). - G. C. Greubel, Sep 29 2022

Mathematica

Table[(1/4374)*(2^(n+4)*(226 +267*n +90*n^2 +9*n^3) +(-1)^n*(758 +555*n +126*n^2 +9*n^3)), {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)

Prog

(Magma) [(1/4374)*(2^(n+4)*(226 +267*n +90*n^2 +9*n^3) +(-1)^n*(758 +555*n +126*n^2 +9*n^3)): n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073373(n): return (1/4374)*(2^(n+4)*(226+267*n+90*n^2+9*n^3) +(-1)^n*(758 +555*n+126*n^2+9*n^3))
[A073373(n) for n in range(40)] # G. C. Greubel, Sep 29 2022

Crossrefs

Fourth (m=3) column of triangle A073370.

Cf. A001045, A073372.

Sequence in context: A212521 A278406 A192069 * A292465 A227162 A057414

Adjacent sequences: A073370 A073371 A073372 * A073374 A073375 A073376

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved