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%I #12 Feb 15 2024 09:38:53
%S 1,11,101,929,8545,78599,722973,6650087,61169169,562649373,5175390189,
%T 47604538285,437878494689,4027716327495,37047945974857,
%U 340776308298291,3134546038698889,28832341420057365,265207115001514409,2439441626426418609,22438596523731989473
%N Number of words of length n over the alphabet {0,1,...,10} such that no two consecutive terms have distance 1.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (11,-14,-28,39,9,-10).
%F For n>6, a(n) = 11*a(n-1) - 14*a(n-2) - 28*a(n-3) + 39*a(n-4) + 9*a(n-5) - 10*a(n-6), a(0)=1, a(1)=11, a(2)=101, a(3)=929, a(4)=8545, a(5)=78599, a(6)=722973.
%F G.f.: (1 - 6*x^2 + 9*x^4 - 2*x^6)/(1 - 11*x + 14*x^2 + 28*x^3 - 39*x^4 - 9*x^5 + 10*x^6).
%t LinearRecurrence[{11, -14, -28, 39, 9, -10}, {1, 11, 101, 929, 8545, 78599, 722973}, 20]
%o (Python)
%o def a(n):
%o .if n in [0,1,2,3,4,5,6]:
%o ..return [1, 11, 101, 929, 8545, 78599, 722973][n]
%o .return 11*a(n-1) - 14*a(n-2) - 28*a(n-3) + 39*a(n-4) + 9*a(n-5) - 10*a(n-6)
%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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