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A124861 Expansion of 1/(1-x-3x^2-4x^3-2x^4). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A027972 A098149 A002878 * A110579 A024829 A296290

Adjacent sequences:  A124858 A124859 A124860 * A124862 A124863 A124864

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 10 2006

STATUS

approved

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Last modified July 2 09:21 EDT 2020. Contains 335398 sequences. (Running on oeis4.)