A190214 Expansion of (1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x).

1, 1, 4, 13, 41, 127, 395, 1232, 3842, 11977, 37336, 116392, 362846, 1131150, 3526285, 10992961, 34269838, 106833983, 333047961, 1038255251, 3236692893, 10090178578, 31455472326, 98060379357, 305696824386, 952989872706, 2970883650186, 9261535631926, 28872232090283

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = Sum_{m=1..n} Sum_{r=m..n} (Sum_{k=m..r} binomial(k,r-k)* Sum_{j=0..m} binomial(j,-3*m+k+2*j)*binomial(m,j))))*binomial(-r+n+m-1,m-1).

Maple

seq(coeftayl((1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x), x = 0, k), k=0..20); # Muniru A Asiru, Feb 01 2018

Mathematica

CoefficientList[Series[(1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x), {x, 0, 50}], x] (* G. C. Greubel, Jan 31 2018 *)

Prog

(Maxima)
a(n):=sum(sum((sum(binomial(k, r-k)*sum(binomial(j, -3*m+k+2*j)*binomial(m, j), j, 0, m), k, m, r))*binomial(-r+n+m-1, m-1), r, m, n), m, 1, n);
(PARI) x='x+O('x^30); Vec((1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x)) \\ G. C. Greubel, Jan 31 2018
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 40); Coefficients(R!((1-x)/(1-x^6-3*x^5-4*x^4-3*x^3-2*x^2-2*x))) // G. C. Greubel, Jan 31 2018

Crossrefs

Sequence in context: A320563 A368344 A268989 * A052529 A049222 A239249

Adjacent sequences: A190211 A190212 A190213 * A190215 A190216 A190217

Keyword

nonn

Author

Vladimir Kruchinin, May 06 2011

Extensions

Terms a(16) onward added by G. C. Greubel, Jan 31 2018

Status

approved