A089074 Expansion of x*(1 + x + x^2)/(1 - 2*x + x^5).

0, 1, 3, 7, 14, 28, 55, 107, 207, 400, 772, 1489, 2871, 5535, 10670, 20568, 39647, 76423, 147311, 283952, 547336, 1055025, 2033627, 3919943, 7555934, 14564532, 28074039, 54114451, 104308959, 201061984, 387559436, 747044833, 1439975215

Offset: 0

Author

Roger L. Bagula, Dec 04 2003

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,-1).

Crossrefs

Cf. A089075, A089076, A089077.

Programs

Magma

R:=PowerSeriesRing(Integers(), 50);
Coefficients(R!( x*(1+x+x^2)/(1-2*x+x^5) )); // G. C. Greubel, Feb 19 2021

Mathematica

CoefficientList[Series[x*(1+x+x^2)/(1-2*x+x^5), {x, 0, 50}], x] (* G. C. Greubel, Feb 19 2021 *)

Sage

def A089074_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( x*(1+x+x^2)/(1-2*x+x^5) ).list()
a=A089074_list(51); a[1:] # G. C. Greubel, Feb 19 2021

Formula

From N. J. A. Sloane, Dec 05 2003: (Start)

G.f.: x*(1+x+x^2)/(1-2*x+x^5).

a(n) = 2*a(n-1) - a(n-5) for n >= 6. (End)

a(n) = A000078(n+4) - 1. - G. C. Greubel, Feb 19 2021

Extensions

Title and offset changed by G. C. Greubel, Feb 19 2021