A122521 Recursion: a(n) = a(n - 6) + a(n - 8).

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 7, 7, 8, 8, 9, 9, 12, 12, 15, 15, 17, 17, 21, 21, 27, 27, 32, 32, 38, 38, 48, 48, 59, 59, 70, 70, 86, 86, 107, 107, 129, 129, 156, 156, 193, 193, 236, 236, 285, 285, 349, 349, 429, 429, 521, 521, 634, 634, 778, 778

Offset: 1

Author

Roger L. Bagula, Sep 16 2006

Keywords

• nonn
• easy

Links

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

Programs

Mathematica

Rest[CoefficientList[Series[-x*(x + 1)*(x^2 - x + 1)*(x^2 + x + 1)/(x^8 + x^6 - 1), {x, 0, 50}], x]] (* G. C. Greubel, May 01 2017 *)

PARI

a(n)=([0,1,0,0,0,0,0,0; 0,0,1,0,0,0,0,0; 0,0,0,1,0,0,0,0; 0,0,0,0,1,0,0,0; 0,0,0,0,0,1,0,0; 0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,1; 1,0,1,0,0,0,0,0]^(n-1)*[1;1;1;1;1;1;1;1])[1,1] \\ Charles R Greathouse IV, Oct 03 2016

PARI

x='x+O('x^50); Vec(-x*(x+1)*(x^2-x+1)*(x^2+x+1)/(x^8+x^6-1)) \\ G. C. Greubel, May 01 2017

Formula

a(n) = a(n - 6) + a(n - 8).

G.f.: -x*(x+1)*(x^2-x+1)*(x^2+x+1)/(x^8+x^6-1). - Colin Barker, Oct 19 2012