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A298806 Growth series for group with presentation < S, T : S^3 = T^6 = (S*T)^6 = 1 >.

%I A298806 #14 Dec 14 2024 14:35:44
%S A298806 1,4,10,25,60,148,358,869,2106,5110,12396,30070,72942,176939,429214,
%T A298806 1041172,2525640,6126607,14861710,36051016,87451296,212136296,
%U A298806 514592810,1248281249,3028037016,7345306340,17817987338,43222250797,104847025002,254334247970,616955127612,1496588180810,3630371290710
%N A298806 Growth series for group with presentation < S, T : S^3 = T^6 = (S*T)^6 = 1 >.
%H A298806 Colin Barker, <a href="/A298806/b298806.txt">Table of n, a(n) for n = 0..1000</a>
%H A298806 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,1,2,-3,2,1,-2,3,-1).
%F A298806 G.f.: (x^10 + x^9 + 2*x^7 - x^6 + 3*x^5 - x^4 + 2*x^3 + x + 1)/(x^10 - 3*x^9 + 2*x^8 - x^7 - 2*x^6 + 3*x^5 - 2*x^4 - x^3 + 2*x^2 - 3*x + 1).
%F A298806 a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4) - 3*a(n-5) + 2*a(n-6) + a(n-7) - 2*a(n-8) + 3*a(n-9) - a(n-10) for n>10. - _Colin Barker_, Feb 06 2018
%o A298806 (Magma) // See Magma program in A298805.
%o A298806 (PARI) Vec((1 - x + x^2)*(1 + x + x^2)*(1 + x - x^2 + x^3 - x^4 + x^5 + x^6) / (1 - 3*x + 2*x^2 - x^3 - 2*x^4 + 3*x^5 - 2*x^6 - x^7 + 2*x^8 - 3*x^9 + x^10) + O(x^40)) \\ _Colin Barker_, Feb 06 2018
%Y A298806 Cf. A008579, A298802, A298805.
%K A298806 nonn,easy
%O A298806 0,2
%A A298806 _John Cannon_ and _N. J. A. Sloane_, Feb 04 2018