A298810 Growth series for group with presentation < S, T : S^2 = T^3 = (S*T)^8 = 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

Author

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

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,3,0,1,0,0,0,-1).

Crossrefs

Cf. A008579, A298802, A298805.

Programs

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

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