A124217 Expansion of (1-x-x^2)/(1-2x-x^2+x^4).

1, 1, 2, 5, 11, 26, 61, 143, 336, 789, 1853, 4352, 10221, 24005, 56378, 132409, 310975, 730354, 1715305, 4028555, 9461440, 22221081, 52188297, 122569120, 287865097, 676078233, 1587833266, 3729175645, 8758319459, 20569736330

Offset: 0

Author

Paul Barry, Oct 19 2006

Keywords

• easy
• nonn

Comments

Diagonal sums of generalized Pascal triangle A124216.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,1,0,-1).

Programs

Mathematica

CoefficientList[Series[(1-x-x^2)/(1-2x-x^2+x^4),{x,0,40}],x] (* or *) LinearRecurrence[{2,1,0,-1},{1,1,2,5},40] (* Harvey P. Dale, Jun 14 2016 *)

Formula

a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k,j)C(j,2(j-k))2^(j-k)}};