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A298810 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^8 = 1 >.

%I A298810 #20 Dec 14 2024 14:34:47
%S A298810 1,3,4,6,8,12,16,24,30,39,50,69,88,120,150,204,260,354,448,609,768,
%T A298810 1047,1328,1806,2284,3108,3930,5352,6776,9219,11662,15873,20082,27336,
%U A298810 34592,47076,59560,81066,102570,139605,176642,240411,304180,414006,523830
%N A298810 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^8 = 1 >.
%H A298810 Colin Barker, <a href="/A298810/b298810.txt">Table of n, a(n) for n = 0..1000</a>
%H A298810 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,3,0,1,0,0,0,-1).
%F A298810 G.f.: (-2*x^14 + 3*x^12 + 3*x^11 + 6*x^10 + 6*x^9 + 9*x^8 + 9*x^7 + 9*x^6 + 9*x^5 + 7*x^4 + 6*x^3 + 4*x^2 + 3*x + 1)/(x^12 - x^8 - 3*x^6 - x^4 +1).
%F A298810 a(n) = a(n-4) + 3*a(n-6) + a(n-8) - a(n-12) for n>12. - _Colin Barker_, Feb 06 2018
%o A298810 (Magma) // See Magma program in A298805.
%o A298810 (PARI) Vec((1 + 3*x + 4*x^2 + 6*x^3 + 7*x^4 + 9*x^5 + 9*x^6 + 9*x^7 + 9*x^8 + 6*x^9 + 6*x^10 + 3*x^11 + 3*x^12 - 2*x^14) / ((1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^4 - x^6 + x^8)) + O(x^60)) \\ _Colin Barker_, Feb 06 2018
%Y A298810 Cf. A008579, A298802, A298805.
%K A298810 nonn,easy
%O A298810 0,2
%A A298810 _John Cannon_ and _N. J. A. Sloane_, Feb 06 2018