OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,7,0,0,8).
FORMULA
a(n) = Sum_{k=0..n} if(mod(n*k, 3)=2, 1, 0) * C(n, k).
a(n) = (2/9)*(2^n-3*0^n+2*(-1)^n)*(1-cos(2*Pi*n/3)).
From Colin Barker, Nov 02 2015: (Start)
a(n) = 7*a(n-3)+8*a(n-6) for n>5.
G.f.: 2*x^2*(2*x^3-3*x^2-1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
(End)
MATHEMATICA
LinearRecurrence[{0, 0, 7, 0, 0, 8}, {0, 0, 2, 0, 6, 10}, 40] (* Harvey P. Dale, Aug 31 2015 *)
PROG
(PARI) concat(vector(2), Vec(2*x^2*(2*x^3-3*x^2-1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100))) \\ Colin Barker, Nov 02 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 08 2003
STATUS
approved