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Expansion of 1 / ((1 - x + x^2)*(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10)).
1

%I #8 Dec 17 2017 10:08:27

%S 1,0,0,0,0,1,1,1,0,0,1,2,2,2,1,1,3,4,5,4,4,5,7,10,11,11,12,15,19,24,

%T 27,30,34,41,51,60,70,80,93,111,133,157,183,213,250,296,350,413,483,

%U 566,666,785,926,1089,1279,1502,1767,2081,2450,2881,3387,3982

%N Expansion of 1 / ((1 - x + x^2)*(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10)).

%H Colin Barker, <a href="/A152067/b152067.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,1,1,0,0,0,0,-1).

%F From _Colin Barker_, Dec 17 2017: (Start)

%F G.f.: 1 / ((1 - x + x^2)*(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10)).

%F a(n) = a(n-5) + a(n-6) + a(n-7) - a(n-12) for n>11.

%F (End)

%t f[x_] = 1 - x^5 - x^6 - x^7 + x^12; g[x] = ExpandAll[x^12*f[1/x]]; a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]

%o (PARI) Vec(1 / ((1 - x + x^2)*(1 + x - x^3 - x^4 - x^5 - x^6 - x^7 + x^9 + x^10)) + O(x^100)) \\ _Colin Barker_, Dec 17 2017

%K nonn,easy

%O 0,12

%A _Roger L. Bagula_, Nov 23 2008

%E New name using Colin Barker's g.f. from _Joerg Arndt_, Dec 17 2017