A117363 Expansion of (1-2x)/(1-x^2+x^3).

1, -2, 1, -3, 3, -4, 6, -7, 10, -13, 17, -23, 30, -40, 53, -70, 93, -123, 163, -216, 286, -379, 502, -665, 881, -1167, 1546, -2048, 2713, -3594, 4761, -6307, 8355, -11068, 14662, -19423, 25730, -34085, 45153, -59815, 79238

Offset: 0

Author

Paul Barry, Mar 10 2006

Keywords

• easy
• sign

Comments

Diagonal sums of number triangle A117362.

Links

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

Crossrefs

Cf. A109248, A007307.

Programs

Mathematica

CoefficientList[Series[(1-2x)/(1-x^2+x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {0,1,-1},{1,-2,1},60] (* Harvey P. Dale, Aug 04 2021 *)

Formula

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