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A087464
Generalized multiplicative Jacobsthal sequence.
3
0, 0, 2, 0, 6, 10, 0, 42, 86, 0, 342, 682, 0, 2730, 5462, 0, 21846, 43690, 0, 174762, 349526, 0, 1398102, 2796202, 0, 11184810, 22369622, 0, 89478486, 178956970, 0, 715827882, 1431655766, 0, 5726623062, 11453246122, 0, 45812984490, 91625968982, 0
OFFSET
0,3
COMMENTS
2^n = A087462(n) + A087463(n) + a(n) provides a decomposition of Pascal's triangle.
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