A377843 - OEIS

%I #17 Nov 10 2024 20:43:52

%S 1,2,9,62,689,7322,69369,616982,5422049,48197042,433434729,3913915502,

%T 35311723409,317999340362,2860994944089,25738114039622,

%U 231602961592769,2084457277181282,18761300850805449,168858054223133342,1519730933499158129,13677470410291063802

%N 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]>.

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-78,210,79,-225).

%F 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)).

%F 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

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

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

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

%K nonn,easy

%O 0,2

%A _Sean A. Irvine_, Nov 09 2024