A193884 Expansion of o.g.f. (1-x^2)/(1-x+x^4).

1, 1, 0, 0, -1, -2, -2, -2, -1, 1, 3, 5, 6, 5, 2, -3, -9, -14, -16, -13, -4, 10, 26, 39, 43, 33, 7, -32, -75, -108, -115, -83, -8, 100, 215, 298, 306, 206, -9, -307, -613, -819, -810, -503, 110, 929, 1739, 2242, 2132, 1203, -536, -2778, -4910, -6113, -5577

Offset: 0

Author

Johannes W. Meijer, Aug 11 2011

Keywords

• sign
• easy

Comments

The Kn11 sums, see A180662, of triangle A108299 equal the terms of this sequence.

Links

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

Crossrefs

Cf. A099530, A108299, A180662.

Programs

Maple

A193884 := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n=2 then 0 elif n=3 then 0 elif n>=4 then procname(n-1)-procname(n-4) fi: end: seq(A193884(n), n=0..54);

Mathematica

CoefficientList[Series[(1-x^2)/(1-x+x^4),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,0,-1},{1,1,0,0},80] (* Harvey P. Dale, Jul 15 2020 *)

Formula

G.f.: (1+x)*(1-x)/(1-x+x^4).

a(n) = a(n-1)-a(n-4), a(0) = a(1) = 1, a(2) = a(3) = 0.

a(n) = A099530(n) - A099530(n-2).