A110513 Expansion of (1 + x)/(1 + 2x + x^3).

1, -1, 2, -5, 11, -24, 53, -117, 258, -569, 1255, -2768, 6105, -13465, 29698, -65501, 144467, -318632, 702765, -1549997, 3418626, -7540017, 16630031, -36678688, 80897393, -178424817, 393528322, -867954037, 1914332891, -4222194104, 9312342245, -20539017381, 45300228866, -99912799977

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• sign

Comments

Diagonal sums of A110511.

Links

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

Crossrefs

A minor variation of A052980.

Programs

Mathematica

CoefficientList[Series[(1+x)/(1+2x+x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {-2,0,-1},{1,-1,2},40] (* Harvey P. Dale, Jun 27 2012 *)

PARI

my(x='x+O('x^50)); Vec((1+x)/(1+2*x+x^3)) \\ G. C. Greubel, Aug 29 2017

Formula

a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-k)} (-1)^(n-k-j)*C(n-k, j)*(-2)^(j-k)*C(k, j-k).

a(0)=1, a(1)=-1, a(2)=2, a(n) = -2*a(n-1) - a(n-3). - Harvey P. Dale, Jun 27 2012