A099530 Expansion of 1/(1 - x + x^4).

1, 1, 1, 1, 0, -1, -2, -3, -3, -2, 0, 3, 6, 8, 8, 5, -1, -9, -17, -22, -21, -12, 5, 27, 48, 60, 55, 28, -20, -80, -135, -163, -143, -63, 72, 235, 378, 441, 369, 134, -244, -685, -1054, -1188, -944, -259, 795, 1983, 2927, 3186, 2391, 408, -2519, -5705, -8096, -8504, -5985, -280, 7816, 16320, 22305, 22585, 14769

Offset: 0

Author

Paul Barry, Oct 20 2004

Keywords

• easy
• sign

Comments

Binomial transform of A099531.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1).

Crossrefs

Cf. A050935, A099531.

Programs

Magma

[n le 4 select 1 else Self(n-1) -Self(n-4): n in [1..81]]; // G. C. Greubel, Apr 13 2023

Mathematica

LinearRecurrence[{1,0,0,-1}, {1,1,1,1}, 80] (* G. C. Greubel, Apr 13 2023 *)

SageMath

@CachedFunction
def a(n): # a = A099530
    if (n<4): return 1
    else: return a(n-1) - a(n-4)
[a(n) for n in range(81)] # G. C. Greubel, Apr 13 2023

Formula

a(n) = a(n-1) - a(n-4).

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k, k)*(-1)^k.