A077941 Expansion of 1/(1-2*x+x^2+x^3).

1, 2, 3, 3, 1, -4, -12, -21, -26, -19, 9, 63, 136, 200, 201, 66, -269, -805, -1407, -1740, -1268, 611, 4230, 9117, 13393, 13439, 4368, -18096, -53999, -94270, -116445, -84621, 41473, 284012, 611172, 896859, 898534, 289037, -1217319, -3622209, -6316136, -7792744, -5647143, 2814594

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Comments

With three leading zeros, is the inverse binomial transform of A077868, with three leading zeros. - Paul Barry, Oct 22 2004

Links

• Index entries for linear recurrences with constant coefficients, signature (2, -1, -1).

Crossrefs

Cf. A077990.

Programs

Mathematica

LinearRecurrence[{2, -1, -1}, {1, 2, 3}, 100] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

PARI

Vec(1/(1-2*x+x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Formula

a(n) = sum{k=0..n+3, C(n+3, k)(-1)^(n+3-k)*sum{j=0..floor((k-2)/2), C(k-2-2j, j+1)}}. - Paul Barry, Oct 22 2004

a(n) = sum{k=0..floor(n/3), C(n+1-k,n-3k)*(-1)^k}. - Tani Akinari, Oct 10 2014