A298806 Growth series for group with presentation < S, T : S^3 = T^6 = (S*T)^6 = 1 >.

1, 4, 10, 25, 60, 148, 358, 869, 2106, 5110, 12396, 30070, 72942, 176939, 429214, 1041172, 2525640, 6126607, 14861710, 36051016, 87451296, 212136296, 514592810, 1248281249, 3028037016, 7345306340, 17817987338, 43222250797, 104847025002, 254334247970, 616955127612, 1496588180810, 3630371290710

Offset: 0

Author

John Cannon and N. J. A. Sloane, Feb 04 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 (3,-2,1,2,-3,2,1,-2,3,-1).

Crossrefs

Cf. A008579, A298802, A298805.

Programs

Magma

// See Magma program in A298805.

PARI

Vec((1 - x + x^2)*(1 + x + x^2)*(1 + x - x^2 + x^3 - x^4 + x^5 + x^6) / (1 - 3*x + 2*x^2 - x^3 - 2*x^4 + 3*x^5 - 2*x^6 - x^7 + 2*x^8 - 3*x^9 + x^10) + O(x^40)) \\ Colin Barker, Feb 06 2018

Formula

G.f.: (x^10 + x^9 + 2*x^7 - x^6 + 3*x^5 - x^4 + 2*x^3 + x + 1)/(x^10 - 3*x^9 + 2*x^8 - x^7 - 2*x^6 + 3*x^5 - 2*x^4 - x^3 + 2*x^2 - 3*x + 1).

a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3) + 2*a(n-4) - 3*a(n-5) + 2*a(n-6) + a(n-7) - 2*a(n-8) + 3*a(n-9) - a(n-10) for n>10. - Colin Barker, Feb 06 2018