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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
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.
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
KEYWORD
nonn,easy
AUTHOR
Sean A. Irvine, Nov 09 2024
STATUS
approved