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

Author

N. J. A. Sloane, Nov 17 2002

Keywords

• nonn
• easy

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1675
• Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 19.
• Index entries for linear recurrences with constant coefficients, signature (3,3,3).

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.

Programs

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 *)

PARI

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

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