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A298810
Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^8 = 1 >.
1
1, 3, 4, 6, 8, 12, 16, 24, 30, 39, 50, 69, 88, 120, 150, 204, 260, 354, 448, 609, 768, 1047, 1328, 1806, 2284, 3108, 3930, 5352, 6776, 9219, 11662, 15873, 20082, 27336, 34592, 47076, 59560, 81066, 102570, 139605, 176642, 240411, 304180, 414006, 523830
OFFSET
0,2
FORMULA
G.f.: (-2*x^14 + 3*x^12 + 3*x^11 + 6*x^10 + 6*x^9 + 9*x^8 + 9*x^7 + 9*x^6 + 9*x^5 + 7*x^4 + 6*x^3 + 4*x^2 + 3*x + 1)/(x^12 - x^8 - 3*x^6 - x^4 +1).
a(n) = a(n-4) + 3*a(n-6) + a(n-8) - a(n-12) for n>12. - Colin Barker, Feb 06 2018
PROG
(Magma) // See Magma program in A298805.
(PARI) Vec((1 + 3*x + 4*x^2 + 6*x^3 + 7*x^4 + 9*x^5 + 9*x^6 + 9*x^7 + 9*x^8 + 6*x^9 + 6*x^10 + 3*x^11 + 3*x^12 - 2*x^14) / ((1 - x + x^2)*(1 + x + x^2)*(1 - x^2 - x^4 - x^6 + x^8)) + O(x^60)) \\ Colin Barker, Feb 06 2018
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
John Cannon and N. J. A. Sloane, Feb 06 2018
STATUS
approved