A077856 Expansion of (1-x)^(-1)/(1-2*x+x^2+x^3).

1, 3, 6, 9, 10, 6, -6, -27, -53, -72, -63, 0, 136, 336, 537, 603, 334, -471, -1878, -3618, -4886, -4275, -45, 9072, 22465, 35904, 40272, 22176, -31823, -126093, -242538, -327159, -285686, -1674, 609498, 1506357, 2404891, 2693928, 1476609, -2145600, -8461736, -16254480, -21901623

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,0,1).

Crossrefs

Cf. A078001.

Programs

Magma

I:=[1,3,6,9]; [n le 4 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-4): n in [1..50]]; // Vincenzo Librandi, May 27 2016

Mathematica

LinearRecurrence[{3, -3, 0, 1}, {1, 3, 6, 9}, 50] (* Vincenzo Librandi, May 27 2016 *)

PARI

Vec((1-x)^(-1)/(1-2*x+x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

Formula

a(n) = Sum_{k=1..floor(n/3+1)} (-1)^k*binomial(n-k+3, 2*k). - Vladeta Jovovic, Feb 10 2003

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-4). - Chai Wah Wu, May 25 2016