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A298812 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^10 = 1 >. 1
1, 3, 4, 6, 8, 12, 16, 24, 32, 48, 62, 87, 114, 165, 216, 312, 408, 588, 766, 1104, 1444, 2082, 2720, 3921, 5122, 7383, 9642, 13902, 18164, 26184, 34204, 49308, 64412, 92856, 121298, 174867, 228438, 329313, 430188, 620160, 810132, 1167888, 1525642, 2199372, 2873104, 4141866, 5410628, 7799973, 10189318, 14688939 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial coefficients for the group  S, T : S^2 = T^3 = (S*T)^m = 1 > approach A029744 as m increases.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,2,0,4,0,2,0,1,0,0,0,-1).

FORMULA

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

a(n) = a(n-4) + 2*a(n-6) + 4*a(n-8) + 2*a(n-10) + a(n-12) - a(n-16) for n>16. - 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 + 10*x^6 + 12*x^7 + 12*x^8 + 12*x^9 + 12*x^10 + 9*x^11 + 9*x^12 + 6*x^13 + 6*x^14 + 3*x^15 + 3*x^16 - 2*x^18) / ((1 + x^2)^2*(1 + x^4)*(1 - 2*x^2 + x^4 - 2*x^6 + x^8)) + O(x^60)) \\ Colin Barker, Feb 06 2018

CROSSREFS

Cf. A008579, A298802, A298805, A299252, A029744.

Sequence in context: A085147 A298810 A298811 * A299252 A299253 A063759

Adjacent sequences:  A298809 A298810 A298811 * A298813 A298814 A298815

KEYWORD

nonn,easy

AUTHOR

John Cannon and N. J. A. Sloane, Feb 06 2018

STATUS

approved

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Last modified January 24 13:24 EST 2020. Contains 331193 sequences. (Running on oeis4.)