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%I #8 Nov 10 2024 20:41:15
%S 1,1,1,1,2,46,496,3004,12872,43912,130816,394384,1470944,6874336,
%T 33550336,151869376,622116992,2353246336,8589869056,31961192704,
%U 125858012672,521796316672,2199022206976,9122012806144,36758056208384,144536687773696,562949936644096
%N Cogrowth sequence of the 16-element group C8 X C2 = <S,T | S^8, T^2, [S,T]>.
%C Gives the even terms, all the odd terms are 0.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-68,112,112,64).
%F G.f.: (8*x^7+28*x^6+42*x^5-34*x^4+35*x^3-21*x^2+7*x-1) / ((4*x-1) * (4*x^2+1) * (4*x^4+8*x^3+8*x^2-4*x+1)).
%e a(4)=2 corresponds to the words SSSSSSSS and TTTTTTTT.
%Y Cf. A007582 (D8), A377627 (C6 X C2), A377714 (C4 X C2).
%K nonn,easy
%O 0,5
%A _Sean A. Irvine_, Nov 09 2024