A299253 - OEIS

A299253

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

1, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 126, 183, 242, 357, 472, 696, 920, 1356, 1792, 2640, 3486, 5136, 6788, 10002, 13216, 19473, 25730, 37911, 50092, 73806, 97518, 143688, 189860, 279744, 369628, 544620, 719612, 1060296, 1400980, 2064243, 2727504, 4018785, 5310068, 7824000, 10337932, 15232200, 20126468

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OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,2,0,3,0,5,0,3,0,2,0,1,0,0,0,-1).

FORMULA

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).

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

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 + 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

CROSSREFS

Cf. A008579, A298802, A298805.

Sequence in context: A298811 A298812 A299252 * A063759 A163978 A145751

Adjacent sequences: A299250 A299251 A299252 * A299254 A299255 A299256

KEYWORD

nonn,easy,changed

AUTHOR

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

STATUS

approved