A117379 Expansion of (1-4x)/(1-x^2+x^3).

1, -4, 1, -5, 5, -6, 10, -11, 16, -21, 27, -37, 48, -64, 85, -112, 149, -197, 261, -346, 458, -607, 804, -1065, 1411, -1869, 2476, -3280, 4345, -5756, 7625, -10101, 13381, -17726, 23482, -31107, 41208

Offset: 0

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A117377.

Links

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

Programs

Mathematica

CoefficientList[Series[(1-4x)/(1-x^2+x^3),{x,0,40}],x] (* or *) LinearRecurrence[ {0,1,-1},{1,-4,1},40] (* Harvey P. Dale, Nov 08 2022 *)

Formula

a(n)=sum{k=0..floor(n/2), (-1)^n*(C(k,n-2k)+4*C(k, n-2k-1))}