A116559 Expansion of g.f. x*(1+x+2*x^2+2*x^3+5*x^4+5*x^5-3*x^6+2*x^7-x^8-x^9)/(1-6*x^6-x^12).

0, 1, 1, 2, 2, 5, 5, 3, 8, 11, 11, 30, 30, 19, 49, 68, 68, 185, 185, 117, 302, 419, 419, 1140, 1140, 721, 1861, 2582, 2582, 7025, 7025, 4443, 11468, 15911, 15911, 43290, 43290, 27379, 70669, 98048, 98048, 266765, 266765, 168717, 435482, 604199, 604199, 1643880, 1643880, 1039681

Offset: 0

Author

Roger L. Bagula, Mar 17 2006

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,6,0,0,0,0,0,1).

Programs

Mathematica

CoefficientList[Series[x*(1 + x + 2*x^2 + 2*x^3 + 5*x^4 + 5*x^5 - 3*x^6 + 2*x^7 - x^8 - x^9)/(1 - 6*x^6 - x^12), {x, 0, 50}], x] (* G. C. Greubel, Sep 20 2017 *)

PARI

x='x+O('x^50); Vec(x*(1 + x + 2*x^2 + 2*x^3 + 5*x^4 + 5*x^5 - 3*x^6 + 2*x^7 - x^8 - x^9)/(1 - 6*x^6 - x^12)) \\ G. C. Greubel, Sep 20 2017

Formula

From R. J. Mathar, Nov 28 2008: (Start)

a(n) = 6*a(n-6) + a(n-12).

G.f.: x*(1+x+2*x^2+2*x^3+5*x^4+5*x^5-3*x^6+2*x^7-x^8-x^9)/(1-6*x^6-x^12).

a(6n+1) = A005667(n). (End)

Extensions

More terms added by G. C. Greubel, Sep 20 2017

Better name using given g.f. from Joerg Arndt, Oct 26 2024