A077879 Expansion of (1-x)^(-1)/(1-2*x^2-2*x^3).

1, 1, 3, 5, 9, 17, 29, 53, 93, 165, 293, 517, 917, 1621, 2869, 5077, 8981, 15893, 28117, 49749, 88021, 155733, 275541, 487509, 862549, 1526101, 2700117, 4777301, 8452437, 14954837, 26459477, 46814549, 82828629, 146548053, 259286357, 458753365, 811668821

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,0,-2).

Formula

a(n) = sum(k=1..n, sum(j=floor((4*k-n)/3)..floor((4*k-n)/2), binomial(j,n-4*k+3*j)*(-1)^(k-j)*binomial(k,j)*2^(n-3*k+2*j))), n>0, a(0)=1. - Vladimir Kruchinin, May 25 2011

Mathematica

CoefficientList[Series[(1-x)^(-1)/(1-2x^2-2x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 2, 0, -2}, {1, 1, 3, 5}, 40] (* Harvey P. Dale, Sep 22 2016 *)

Prog

(Maxima)
a(n):=sum(sum(binomial(j, n-4*k+3*j)*(-1)^(k-j)*binomial(k, j)*2^(n-3*k+2*j), j, floor((4*k-n)/3), floor((4*k-n)/2)), k, 1, n), /* Vladimir Kruchinin, May 25 2011 */

Crossrefs

Sequence in context: A287207 A298338 A018162 * A078140 A279780 A289260

Adjacent sequences: A077876 A077877 A077878 * A077880 A077881 A077882

Keyword

nonn

Author

N. J. A. Sloane, Nov 17 2002

Status

approved