A077840 Expansion of (1-x)/(1-2*x-3*x^2-3*x^3).

1, 1, 5, 16, 50, 163, 524, 1687, 5435, 17503, 56372, 181558, 584741, 1883272, 6065441, 19534921, 62915981, 202633048, 652618802, 2101884691, 6769524932, 21802560343, 70219349555, 226154954935, 728375639564, 2345874192598, 7555340168693, 24333429833872

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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

Formula

a(0)=1 and, for n >= 1, a(n) = Sum(k=1..n, Sum(i=k..n,(Sum(j=0..k, binomial(j,-3*k+2*j+i)*3^(-2*k+j+i)*binomial(k,j)))*binomial(n+k-i-1,k-1))). - Vladimir Kruchinin, May 05 2011

a(0)=1, a(1)=1, a(2)=5, a(n) = 2*a(n-1) + 3*a(n-2) + 3*a(n-3). - Harvey P. Dale, Aug 19 2014

Mathematica

CoefficientList[Series[(1-x)/(1-2x-3x^2-3x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 3, 3}, {1, 1, 5}, 30] (* Harvey P. Dale, Aug 19 2014 *)

Prog

(Maxima)
a(n):=sum(sum((sum(binomial(j, -3*k+2*j+i)*3^(-2*k+j+i)*binomial(k, j), j, 0, k))*binomial(n+k-i-1, k-1), i, k, n), k, 1, n); /* Vladimir Kruchinin, May 05 2011 */

Crossrefs

Sequence in context: A027108 A304168 A317817 * A007343 A371437 A274492

Adjacent sequences: A077837 A077838 A077839 * A077841 A077842 A077843

Keyword

nonn

Author

N. J. A. Sloane, Nov 17 2002

Status

approved