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%I #13 Sep 08 2022 08:46:20
%S 1,4,8,16,32,64,126,242,472,920,1792,3486,6788,13216,25730,50092,
%T 97518,189860,369628,719612,1400980,2727504,5310068,10337932,20126468,
%U 39183340,76284330,148514636,289136638,562907480,1095899956,2133559698,4153734080,8086723216,15743687792,30650697262,59672502090
%N Growth series for group with presentation < S, T : S^3 = T^3 = (S*T)^6 = 1 >.
%H Colin Barker, <a href="/A298807/b298807.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,2,3,5,3,2,1,0,-1).
%F G.f.: (-2*x^11 + 3*x^10 + 6*x^9 + 9*x^8 + 12*x^7 + 15*x^6 + 15*x^5 + 13*x^4 + 10*x^3 + 7*x^2 + 4*x + 1)/(x^10 - x^8 - 2*x^7 - 3*x^6 - 5*x^5 - 3*x^4 - 2*x^3 - x^2 + 1).
%F a(n) = a(n-2) + 2*a(n-3) + 3*a(n-4) + 5*a(n-5) + 3*a(n-6) + 2*a(n-7) + a(n-8) - a(n-10) for n>11. - _Colin Barker_, Feb 06 2018
%o (Magma) See Magma program in A298805.
%o (PARI) Vec((1 + 4*x + 7*x^2 + 10*x^3 + 13*x^4 + 15*x^5 + 15*x^6 + 12*x^7 + 9*x^8 + 6*x^9 + 3*x^10 - 2*x^11) / ((1 + x + x^2 + x^3 + x^4)*(1 - x - x^2 - x^3 - x^4 - x^5 + x^6)) + O(x^40)) \\ _Colin Barker_, Feb 06 2018
%Y Cf. A008579, A298802, A298805.
%K nonn,easy
%O 0,2
%A _John Cannon_ and _N. J. A. Sloane_, Feb 04 2018
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