A117576 - OEIS

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A117576

Expansion of (1-x^3)/((1-x^2)(1+2x^2)).

1, 0, -1, -1, 3, 1, -5, -3, 11, 5, -21, -11, 43, 21, -85, -43, 171, 85, -341, -171, 683, 341, -1365, -683, 2731, 1365, -5461, -2731, 10923, 5461, -21845, -10923, 43691, 21845, -87381, -43691, 174763, 87381, -349525, -174763, 699051

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

A signed pair-reversal of the Jacobsthal numbers A001045. Diagonal sums of A116949.

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (-1,-2,-2).

FORMULA

G.f.: (1+x+x^2)/(1+x+2x^2+2x^3); a(n)=-a(n-1)-2a(n-2)-2a(n-3); a(n)=2^(n/2)(2*cos(pi*n/2)/3+sqrt(2)*sin(pi*n/2)/6)+(-1)^n/3;

a(n) = floor(((-1)^(floor(n/2))*2^(2*floor(n/2)+1-floor((n+1)/2))+1)/3). - Tani Akinari, Nov 09 2012

CROSSREFS