A117374 Expansion of (1-3x)/(1-x^2+x^3).

1, -3, 1, -4, 4, -5, 8, -9, 13, -17, 22, -30, 39, -52, 69, -91, 121, -160, 212, -281, 372, -493, 653, -865, 1146, -1518, 2011, -2664, 3529, -4675, 6193, -8204, 10868, -14397, 19072, -25265, 33469

Offset: 0

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A117372.

Links

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

Programs

Mathematica

CoefficientList[Series[(1-3x)/(1-x^2+x^3),{x,0,40}],x] (* or *) LinearRecurrence[{0,1,-1},{1,-3,1},40] (* Harvey P. Dale, May 06 2022 *)

Formula

a(n)=a(n-2)+a(n-3); a(n)=sum{k=0..floor(n/2), (-1)^n*(C(k,n-2k)+3*C(k, n-2k-1))}.