A190214 - OEIS

%I #14 Oct 02 2023 13:35:53

%S 1,1,4,13,41,127,395,1232,3842,11977,37336,116392,362846,1131150,

%T 3526285,10992961,34269838,106833983,333047961,1038255251,3236692893,

%U 10090178578,31455472326,98060379357,305696824386,952989872706,2970883650186,9261535631926,28872232090283

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

%H G. C. Greubel, <a href="/A190214/b190214.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, 3, 4, 3, 1).

%F 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).

%p 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

%t 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 *)

%o (Maxima)

%o 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);

%o (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

%o (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

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, May 06 2011

%E Terms a(16) onward added by _G. C. Greubel_, Jan 31 2018