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 A299253 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^12 = 1 >. 1

%I

%S 1,3,4,6,8,12,16,24,32,48,64,96,126,183,242,357,472,696,920,1356,1792,

%T 2640,3486,5136,6788,10002,13216,19473,25730,37911,50092,73806,97518,

%U 143688,189860,279744,369628,544620,719612,1060296,1400980,2064243,2727504,4018785,5310068,7824000,10337932,15232200,20126468

%N Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^12 = 1 >.

%H Colin Barker, <a href="/A299253/b299253.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1,0,2,0,3,0,5,0,3,0,2,0,1,0,0,0,-1).

%F G.f.: (-2*x^22 + 3*x^20 + 3*x^19 + 6*x^18 + 6*x^17 + 9*x^16 + 9*x^15 + 12*x^14 + 12*x^13 + 15*x^12 + 15*x^11 + 15*x^10 + 15*x^9 + 13*x^8 + 12*x^7 + 10*x^6 + 9*x^5 + 7*x^4 + 6*x^3 + 4*x^2 + 3*x + 1)/(x^20 - x^16 - 2*x^14 - 3*x^12 - 5*x^10 - 3*x^8 - 2*x^6 - x^4 + 1).

%F a(n) = a(n-4) + 2*a(n-6) + 3*a(n-8) + 5*a(n-10) + 3*a(n-12) + 2*a(n-14) + a(n-16) - a(n-20) for n>20. - _Colin Barker_, Feb 06 2018

%o (MAGMA) See Magma program in A298805.

%o (PARI) Vec((1 + 3*x + 4*x^2 + 6*x^3 + 7*x^4 + 9*x^5 + 10*x^6 + 12*x^7 + 13*x^8 + 15*x^9 + 15*x^10 + 15*x^11 + 15*x^12 + 12*x^13 + 12*x^14 + 9*x^15 + 9*x^16 + 6*x^17 + 6*x^18 + 3*x^19 + 3*x^20 - 2*x^22) / ((1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)*(1 - x^2 - x^4 - x^6 - x^8 - x^10 + x^12)) + O(x^60)) \\ _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 06 2018

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Last modified January 28 22:35 EST 2020. Contains 331328 sequences. (Running on oeis4.)