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A299252 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^11 = 1 >. 2
1, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 94, 120, 178, 232, 344, 448, 664, 864, 1280, 1662, 2459, 3202, 4741, 6168, 9132, 11880, 17588, 22880, 33870, 44068, 65246, 84880, 125664, 163484, 242036, 314880, 466176, 606478, 897892, 1168124, 1729394, 2249880, 3330929, 4333418, 6415591, 8346452, 12356856, 16075828, 23800132 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (-1,0,0,1,1,2,2,3,4,3,2,3,2,3,2,3,2,3,4,3,2,2,1,1,0,0,-1,-1).

FORMULA

G.f.: (-2*x^30 - 2*x^29 + 3*x^28 + 6*x^27 + 9*x^26 + 12*x^25 + 15*x^24 + 18*x^23 + 21*x^22 + 24*x^21 + 27*x^20 + 31*x^19 + 33*x^18 + 33*x^17 + 33*x^16 + 33*x^15 + 33*x^14 + 33*x^13 + 33*x^12 + 33*x^11 + 29*x^10 + 27*x^9 + 25*x^8 + 22*x^7 + 19*x^6 + 16*x^5 + 13*x^4 + 10*x^3 + 7*x^2 + 4*x + 1)/(x^28 + x^27 - x^24 - x^23 - 2*x^22 - 2*x^21 - 3*x^20 - 4*x^19 - 3*x^18 - 2*x^17 - 3*x^16 - 2*x^15 - 3*x^14 - 2*x^13 - 3*x^12 - 2*x^11 - 3*x^10 - 4*x^9 - 3*x^8 - 2*x^7 - 2*x^6 - x^5 - x^4 + x + 1).

a(n) = -a(n-1) + a(n-4) + a(n-5) + 2*a(n-6) + 2*a(n-7) + 3*a(n-8) + 4*a(n-9) + 3*a(n-10) + 2*a(n-11) + 3*a(n-12) + 2*a(n-13) + 3*a(n-14) + 2*a(n-15) + 3*a(n-16) + 2*a(n-17) + 3*a(n-18) + 4*a(n-19) + 3*a(n-20) + 2*a(n-21) + 2*a(n-22) + a(n-23) + a(n-24) - a(n-27) - a(n-28) for n>30. - 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 + 16*x^5 + 19*x^6 + 22*x^7 + 25*x^8 + 27*x^9 + 29*x^10 + 33*x^11 + 33*x^12 + 33*x^13 + 33*x^14 + 33*x^15 + 33*x^16 + 33*x^17 + 33*x^18 + 31*x^19 + 27*x^20 + 24*x^21 + 21*x^22 + 18*x^23 + 15*x^24 + 12*x^25 + 9*x^26 + 6*x^27 + 3*x^28 - 2*x^29 - 2*x^30) / ((1 + x + x^2)*(1 + x^3 + x^6)*(1 - x^2 - x^4 - x^6 - x^8 + x^10 - x^12 - x^14 - x^16 - x^18 + x^20)) + O(x^60)) \\ Colin Barker, Feb 06 2018

CROSSREFS

Cf. A008579, A298802, A298805.

Sequence in context: A298810 A298811 A298812 * A299253 A063759 A163978

Adjacent sequences:  A299249 A299250 A299251 * A299253 A299254 A299255

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified September 18 17:45 EDT 2019. Contains 327178 sequences. (Running on oeis4.)