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

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn

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).

Programs

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 *)

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 */

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