|
%I #8 Jun 07 2017 13:10:33
%S 1,10,88,776,6844,60364,532412,4695892,41417932,365307620,3222026092,
%T 28418383780,250651147340,2210751960772,19498910274028,
%U 171981076403492,1516879160180620,13378927697789188,118002614210453804,1040787219651555556,9179779989094951372
%N Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 4.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9, 0, -14).
%F For n>3, a(n) = 9*a(n-1) - 14*a(n-3), a(0)=1, a(1)=10, a(2)=88, a(3)=776.
%F G.f.: (1 + x - 2*x^2 - 2*x^3)/(1 - 9*x + 14*x^3).
%t LinearRecurrence[{9, 0, -14}, {1, 10, 88, 776}, 30]
%o (Python)
%o def a(n):
%o .if n in [0, 1, 2, 3]:
%o ..return [1, 10, 88, 776][n]
%o .return 9*a(n-1)-14*a(n-3)
%Y Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.
%K nonn,easy
%O 0,2
%A _David Nacin_, Jun 02 2017
|
