A077828 Expansion of 1/(1-3*x-3*x^2-3*x^3).

1, 3, 12, 48, 189, 747, 2952, 11664, 46089, 182115, 719604, 2843424, 11235429, 44395371, 175422672, 693160416, 2738935377, 10822555395, 42763953564, 168976333008, 667688525901, 2638286437419, 10424853888984, 41192486556912, 162766880649945, 643152663287523

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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

Formula

a(n)=sum{k=0..n, T(n-k, k)3^(n-k)}, T(n, k) = trinomial coefficients (A027907). - Paul Barry, Feb 15 2005

a(n)=sum{k=0..n, sum{i=0..floor((n-k)/2), C(n-k-i, i)C(k, n-k-i)}*3^k}; - Paul Barry, Apr 26 2005

Mathematica

CoefficientList[Series[1/(1-3x-3x^2-3x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[ {3, 3, 3}, {1, 3, 12}, 30] (* Harvey P. Dale, Dec 25 2018 *)

Prog

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

Crossrefs

Partial sums of S(n, x), for x=1...12, A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420, A097784, A097826-7.

Cf. A071675.

Sequence in context: A064562 A259865 A254942 * A164346 A002001 A113956

Adjacent sequences: A077825 A077826 A077827 * A077829 A077830 A077831

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved