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%I #21 Sep 08 2022 08:46:15
%S 1,4,9,17,30,51,84,135,215,341,538,846,1328,2082,3262,5108,7997,12519,
%T 19595,30668,47996,75112,117546,183950,287864,450478,704950,1103170,
%U 1726339,2701526,4227582,6615684,10352789,16200930,25352598,39673907,62085111,97156070
%N G.f. = b(2)*b(6)*b(10)/(x^14+x^12-x^5-x^3-x+1), where b(k) = (1-x^k)/(1-x).
%C This is the Poincaré series [or Poincare series] for the quasi-Lannér diagram QL4_3 - see Tables 7.6, 7.7 and 7.8 in Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2009), or equivalently Tables 5 and 6 in the shorter version, Maxim Chapovalov, Dimitry Leites and Rafael Stekolshchik (2010).
%H Colin Barker, <a href="/A266334/b266334.txt">Table of n, a(n) for n = 0..1000</a>
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="https://arxiv.org/abs/0906.1596">The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, arXiv:0906.1596 [math.RT], 2009.
%H Maxim Chapovalov, Dimitry Leites, and Rafael Stekolshchik, <a href="http://dx.doi.org/10.1142/S1402925110000842">The Poincaré series [or Poincare series] of the hyperbolic Coxeter groups with finite volume of fundamental domains</a>, Journal of Nonlinear Mathematical Physics 17.supp01 (2010), 169-215.
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,0,1,0,0,0,0,0,0,-1,0,-1).
%p gf:= b(2)*b(6)*b(10)/(x^14+x^12-x^5-x^3-x+1):
%p b:= k->(1-x^k)/(1-x):
%p a:= n-> coeff(series(gf, x, n+1), x, n):
%p seq(a(n), n=0..40);
%t b[k_] := (1 - x^k)/(1 - x); CoefficientList[Series[b[2] b[6] b[10]/(x^14 + x^12 - x^5 - x^3 - x + 1), {x, 0, 40}], x] (* _Bruno Berselli_, Dec 29 2015 *)
%o (Magma) /* By definition: */ m:=40; R<x>:=PowerSeriesRing(Integers(), m); b:=func<k|(1-x^k)/(1-x)>; Coefficients(R!(b(2)*b(6)*b(10)/(x^14+x^12-x^5-x^3-x+1))); // _Bruno Berselli_, Dec 29 2015
%Y Cf. similar sequences listed in A265055.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Dec 27 2015