A087463 Generalized multiplicative Jacobsthal sequence.

0, 1, 1, 0, 5, 11, 0, 43, 85, 0, 341, 683, 0, 2731, 5461, 0, 21845, 43691, 0, 174763, 349525, 0, 1398101, 2796203, 0, 11184811, 22369621, 0, 89478485, 178956971, 0, 715827883, 1431655765, 0, 5726623061, 11453246123, 0, 45812984491, 91625968981, 0

Offset

0,5

Comments

Set A001045(3n)=0 in A001045.

2^n = A087462(n) + a(n) + A087464(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)=1, 1, 0)*C(n, k).

a(n) = (2/9)*(1-cos(2*Pi*n/3))*(2^n-(-1)^n).

From Colin Barker, Nov 02 2015: (Start)

a(n) = 7*a(n-3)+8*a(n-6) for n>5.

G.f.: -x*(4*x^4-2*x^3+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).

(End)

Prog

(PARI) concat(0, Vec(-x*(4*x^4-2*x^3+x+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

Sequence in context: A309558 A346104 A383269 * A160366 A160923 A201457

Adjacent sequences: A087460 A087461 A087462 * A087464 A087465 A087466

Keyword

easy,nonn

Author

Paul Barry, Sep 08 2003

Status

approved