A124861 Expansion of 1/(1-x-3x^2-4x^3-2x^4).

1, 1, 4, 11, 29, 80, 219, 597, 1632, 4459, 12181, 33280, 90923, 248405, 678656, 1854123, 5065557, 13839360, 37809835, 103298389, 282216448, 771029675, 2106492245, 5755043840, 15723072171, 42956232021, 117358608384

Offset

0,3

Comments

Diagonal sums of number triangle A124860.

Links

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (1, 3, 4, 2).

Formula

a(n)=a(n-1)+3a(n-2)+4a(n-3)+2a(n-4); a(n)=sum{k=0..floor(n/2), J(n-k+1)C(n-k,k)} where J(n)=A001045(n). - corrected by Harvey P. Dale, Apr 22 2011

G.f.: 1 + x/(G(0) - x) where G(k) = 1 - 8*x - 2*k*x + k + 2*x*(k+1)*(k+5)/G(k+1); (continued fraction). - Sergei N. Gladkovskii, Apr 09 2013

Mathematica

LinearRecurrence[{1, 3, 4, 2}, {1, 1, 4, 11}, 30] (* or *) CoefficientList[ Series[ 1/(1-x-3x^2-4x^3-2x^4), {x, 0, 30}], x] (* Harvey P. Dale, Apr 22 2011 *)

Crossrefs

Sequence in context: A098149 A002878 A341341 * A369844 A351438 A110579

Adjacent sequences: A124858 A124859 A124860 * A124862 A124863 A124864

Keyword

easy,nonn

Author

Paul Barry, Nov 10 2006

Status

approved