A087464 Generalized multiplicative Jacobsthal sequence.

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.

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

Cf. A001045, A087462, A087463.

Sequence in context: A003076 A175478 A011123 * A078048 A362186 A335061

Adjacent sequences: A087461 A087462 A087463 * A087465 A087466 A087467

Keyword

easy,nonn

Author

Paul Barry, Sep 08 2003

Status

approved