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

Author

Wolfdieter Lang, Aug 02 2002

Keywords

• nonn
• easy

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).

Crossrefs

Tenth (m=9) column of triangle A073370.

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

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^10 )); // G. C. Greubel, Oct 01 2022

Mathematica

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

SageMath

def A073379_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/((1+x)*(1-2*x))^10 ).list()
A073379_list(40) # G. C. Greubel, Oct 01 2022

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.