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%I #17 Nov 10 2024 20:42:57
%S 1,1,1,2,29,211,926,3095,9829,37130,164921,728575,2973350,11450531,
%T 43942081,174174002,708653429,2884834891,11582386286,46006694735,
%U 182670807229,729520967450,2926800830801,11743814559415,47006639297270,187791199242011,750176293590361
%N Cogrowth sequence of the 12-element group C6 X C2 = <S,T | S^6, T^2, [S,T]>.
%C Gives the even terms, all the odd terms are 0.
%F G.f.: (6*x^5+5*x^4+11*x^3-10*x^2+5*x-1) / ((4*x-1) * (x^2+x+1) * (9*x^2-3*x+1)).
%e a(2)=1 corresponds to the word TTTT.
%e a(3)=2 corresponds to the words SSSSSS and TTTTTT.
%Y Cf. A007583 (D6), A377626 (A4), A377656 (Dic12), A377714 (C4 X C2), A377840 (C8 X C2).
%K nonn,easy
%O 0,4
%A _Sean A. Irvine_, Nov 02 2024