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%I #13 Feb 15 2024 08:56:59
%S 1,11,109,1081,10721,106329,1054553,10458881,103729441,1028771337,
%T 10203182953,101193470929,1003620008177,9953736259545,98719500126905,
%U 979083577381409,9710388021269185,96306012787788969,955147011506293513,9472989143467878769,93951530216004879761
%N Number of words over the alphabet {0,1,...,10} such that no two consecutive terms have distance 5.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-18).
%F For n>3, a(n) = 10*a(n-1) + a(n-2) - 18*a(n-3), a(0)=1, a(1)=11, a(2)=109, a(3)=1081.
%F G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 10*x - x^2 + 18*x^3).
%t LinearRecurrence[{10, 1, -18}, {1, 11, 109, 1081}, 20]
%o (Python)
%o def a(n):
%o .if n in [0,1,2,3]:
%o ..return [1, 11, 109, 1081][n]
%o .return 10*a(n-1) + a(n-2) - 18*a(n-3)
%Y Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.
%K nonn,easy
%O 0,2
%A _David Nacin_, Jun 07 2017
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