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%I #26 Feb 16 2024 17:18:12
%S 1,9,75,627,5241,43809,366195,3060987,25586481,213874809,1787757915,
%T 14943687747,124912775721,1044133269009,8727804479235,72954835640907,
%U 609822098564961,5097441295442409,42608996659234155,356164297160200467
%N Numbers of words on alphabet {0,1,...,8} with no subwords ii, where i is from {0,1,...,5}.
%C a(n) is the number of nonary sequences of length n such that no two consecutive terms have distance 6. - _David Nacin_, May 31 2017
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,3).
%F G.f.: (1 + x)/(1 - 8*x -3*x^2).
%F a(n) = 8*a(n-1) + 3*a(n-2) with n>1, a(0) = 1, a(1) = 9.
%F a(n) = ((1+t)*(4-t)^(n+1)+(-1+t)*(4+t)^(n+1))/(6*t), where t=sqrt(19). [_Bruno Berselli_, Feb 04 2015]
%t RecurrenceTable[{a[0] == 1, a[1] == 9, a[n] == 8 a[n - 1] + 3 a[n - 2]}, a[n], {n, 0, 20}]
%t LinearRecurrence[{8,3},{1,9},20] (* _Harvey P. Dale_, Feb 16 2024 *)
%o (Magma) [n le 1 select 9^n else 8*Self(n)+3*Self(n-1): n in [0..20]];
%Y Cf. A015574, A055099, A126473, A126501, A126528, A254598, A254602.
%K nonn,easy
%O 0,2
%A _Milan Janjic_, Feb 04 2015
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