A377843 Cogrowth sequence of the 16-element group C4 X C2 X C2 = <S,T,U | S^4, T^2, U^2, [S,T], [S,U], [T,U]>.

1, 2, 9, 62, 689, 7322, 69369, 616982, 5422049, 48197042, 433434729, 3913915502, 35311723409, 317999340362, 2860994944089, 25738114039622, 231602961592769, 2084457277181282, 18761300850805449, 168858054223133342, 1519730933499158129, 13677470410291063802

Offset

0,2

Comments

Gives the even terms, all the odd terms are 0.

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (15,-78,210,79,-225).

Formula

G.f.: (38*x^4+127*x^3-57*x^2+13*x-1) / ((1-x) * (9*x-1) * (x+1) * (25*x^2-6*x+1)).

E.g.f.: (2*exp(3*x)*cos(4*x) + 5*cosh(x) + cosh(9*x) + sinh(x) + sinh(9*x))/8. - Stefano Spezia, Nov 10 2024

Example

a(2)=9 corresponds to the words SSSS, TTTT, UUUU, TTUU, TUUT, UUTT, TUTU, UTUT, UTTU.

Mathematica

LinearRecurrence[{15, -78, 210, 79, -225}, {1, 2, 9, 62, 689}, 22] (* James C. McMahon, Nov 10 2024 *)

Crossrefs

Cf. A070775 (C4 X C4), A377714 (C4 X C2), A377840 (C8 X C2), A007582 (D8).

Sequence in context: A213528 A100262 A166886 * A212413 A003577 A085928

Adjacent sequences: A377840 A377841 A377842 * A377844 A377845 A377846

Keyword

nonn,easy

Author

Sean A. Irvine, Nov 09 2024

Status

approved