A077826 Expansion of (1-x)^(-1)/(1-2*x-3*x^2-2*x^3).

1, 3, 10, 32, 101, 319, 1006, 3172, 10001, 31531, 99410, 313416, 988125, 3115319, 9821846, 30965900, 97627977, 307797347, 970410426, 3059468848, 9645763669, 30410754735, 95877738174, 302279267892, 953013259777, 3004619799579, 9472837914274, 29865561746840

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,1,-1,-2).

Crossrefs

Partial sums of S(n, x), for x=1...10, A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420, A097784.

Partial sums of A077833.

Programs

Mathematica

LinearRecurrence[{3,1,-1,-2},{1,3,10,32},30] (* Harvey P. Dale, May 12 2024 *)

PARI

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

Formula

From Wesley Ivan Hurt, Jun 26 2022: (Start)

G.f.: (1-x)^(-1)/(1-2*x-3*x^2-2*x^3).

a(n) = 3*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4). (End)