A077829 Expansion of 1/(1-3*x-3*x^2-2*x^3).

1, 3, 12, 47, 183, 714, 2785, 10863, 42372, 165275, 644667, 2514570, 9808261, 38257827, 149227404, 582072215, 2270414511, 8855914986, 34543132921, 134737972743, 525555146964, 2049965624963, 7996038261267, 31189121952618, 121655411891581, 474525678055131

Offset: 0

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

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

Crossrefs

Partial sums of S(n, x), for x=1...14, A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420, A097784, A097826-A097828, A076139.

Programs

Mathematica

CoefficientList[Series[1/(1 - 3*x - 3*x^2 - 2*x^3), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 20 2024 *)
LinearRecurrence[{3,3,2},{1,3,12},30] (* Harvey P. Dale, Dec 20 2024 *)

PARI

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

Formula

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

a(n) = 3*a(n-1) + 3*a(n-2) + 2*a(n-3). - Wesley Ivan Hurt, Jan 20 2024