A073379 Ninth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself.

1, 10, 75, 440, 2255, 10362, 43945, 174460, 656370, 2359500, 8158722, 27275040, 88524930, 279892380, 864508590, 2614740216, 7759693095, 22634343270, 64990287285, 183929970840, 513661549401, 1416970676550

Offset

0,2

Comments

For a(n) in terms of U(n+1) and U(n), with U(n) = A001045(n+1), see A073370 and the row polynomials of triangles A073399 and A073400.

Links

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

Index entries for linear recurrences with constant coefficients, signature (10,-25,-60,330,12,-1770,960,5835,-4070,-13597, 8140,23340,-7680,-28320,-384,21120,7680,-6400,-5120,-1024).

Formula

a(n) = Sum_{k=0..n} (b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073378(k).

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9) * binomial(n-k, k) * 2^k.

G.f.: 1/(1-(1+2*x)*x)^10 = 1/((1+x)*(1-2*x))^10.

Mathematica

CoefficientList[Series[1/((1+x)*(1-2*x))^10, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^10 )); // G. C. Greubel, Oct 01 2022
(SageMath)
def A073379_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x)*(1-2*x))^10 ).list()
A073379_list(40) # G. C. Greubel, Oct 01 2022

Crossrefs

Tenth (m=9) column of triangle A073370.

Cf. A001045, A073370, A073378, A073399, A073400.

Sequence in context: A026969 A026979 A274251 * A283238 A316462 A022734

Adjacent sequences: A073376 A073377 A073378 * A073380 A073381 A073382

Keyword

nonn,easy

Author

Wolfdieter Lang, Aug 02 2002

Status

approved