OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Milan Janjic, Hessenberg Matrices and Integer Sequences , J. Int. Seq. 13 (2010) # 10.7.8.
Index entries for linear recurrences with constant coefficients, signature (10,-35,40,30,-68,-30,40,35,10,1).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(n-k+4, 4) * binomial(n-k, k).
a(n) = ((2457 +2128*n +572*n^2 +48*n^3)*(n+1)*U(n+1) + 5*(123 +142*n +44*n^2 +4*n^3) *(n+2)*U(n))/(3*2^11), with U(n) = A000129(n+1), n>=0.
G.f.: 1/(1-(2+x)*x)^5.
a(n) = F''''(n+5, 2)/4!, that is, 1/4! times the 4th derivative of the (n+5)th Fibonacci polynomial evaluated at x=2. - T. D. Noe, Jan 19 2006
MATHEMATICA
CoefficientList[Series[1/(1-2*x-x^2)^5, {x, 0, 40}], x] (* G. C. Greubel, Oct 02 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-x^2)^5 )); // G. C. Greubel, Oct 02 2022
(SageMath)
def A073381_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-2*x-x^2)^5 ).list()
A073381_list(40) # G. C. Greubel, Oct 02 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved