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

0,4

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).

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)

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 *)

Prog

(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

Crossrefs

Sequence in context: A045537 A243941 A161622 * A210802 A257943 A008280

Adjacent sequences: A116556 A116557 A116558 * A116560 A116561 A116562

Keyword

nonn,easy,less

Author

Roger L. Bagula, Mar 17 2006

Extensions

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

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

Status

approved