A298811 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^9 = 1 >.

1, 3, 4, 6, 8, 12, 16, 24, 32, 46, 56, 82, 104, 152, 192, 280, 350, 507, 642, 933, 1176, 1708, 2152, 3122, 3940, 5726, 7216, 10480, 13212, 19188, 24190, 35140, 44300, 64338, 81112, 117809, 148522, 215717, 271960, 394998, 497972, 723268, 911828, 1324360, 1669626, 2425008, 3057212, 4440362, 5597988, 8130648

Offset

0,2

Links

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

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

Formula

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

Crossrefs

Cf. A008579, A298802, A298805.

Sequence in context: A085147 A367398 A298810 * A298812 A299252 A299253

Adjacent sequences: A298808 A298809 A298810 * A298812 A298813 A298814

Keyword

nonn,easy

Author

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

Status

approved