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A298807 Growth series for group with presentation < S, T : S^3 = T^3 = (S*T)^6 = 1 >.

%I A298807 #19 Jul 02 2025 17:05:06
%S A298807 1,4,8,16,32,64,126,242,472,920,1792,3486,6788,13216,25730,50092,
%T A298807 97518,189860,369628,719612,1400980,2727504,5310068,10337932,20126468,
%U A298807 39183340,76284330,148514636,289136638,562907480,1095899956,2133559698,4153734080,8086723216,15743687792,30650697262,59672502090
%N A298807 Growth series for group with presentation < S, T : S^3 = T^3 = (S*T)^6 = 1 >.
%H A298807 Colin Barker, <a href="/A298807/b298807.txt">Table of n, a(n) for n = 0..1000</a>
%H A298807 <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 A298807 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 A298807 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
%t A298807 LinearRecurrence[{0,1,2,3,5,3,2,1,0,-1},{1,4,8,16,32,64,126,242,472,920,1792,3486},40] (* _Harvey P. Dale_, Jul 02 2025 *)
%o A298807 (Magma) // See Magma program in A298805.
%o A298807 (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 A298807 Cf. A008579, A298802, A298805.
%K A298807 nonn,easy
%O A298807 0,2
%A A298807 _John Cannon_ and _N. J. A. Sloane_, Feb 04 2018