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A298807
Growth series for group with presentation < S, T : S^3 = T^3 = (S*T)^6 = 1 >.
1
1, 4, 8, 16, 32, 64, 126, 242, 472, 920, 1792, 3486, 6788, 13216, 25730, 50092, 97518, 189860, 369628, 719612, 1400980, 2727504, 5310068, 10337932, 20126468, 39183340, 76284330, 148514636, 289136638, 562907480, 1095899956, 2133559698, 4153734080, 8086723216, 15743687792, 30650697262, 59672502090
OFFSET
0,2
FORMULA
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).
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
PROG
(Magma) See Magma program in A298805.
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Feb 04 2018
STATUS
approved