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A287825 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 1.

%I A287825 #15 Apr 09 2020 08:41:40
%S A287825 1,10,82,674,5540,45538,374316,3076828,25291120,207889674,1708825732,
%T A287825 14046322404,115458919774,949057110644,7801124426174,64124215108032,
%U A287825 527092600834054,4332631742719370,35613662169258228,292739611493034596,2406281042646218328
%N A287825 Number of sequences over the alphabet {0,1,...,9} such that no two consecutive terms have distance 1.
%H A287825 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9, -4, -21, 9, 5).
%F A287825 For n>5, a(n) = 9*a(n-1) - 4*a(n-2) - 21*a(n-3) + 9*a(n-4) + 5*a(n-5), a(0)=1, a(1)=10, a(2)=82, a(3)=674, a(4)=5540, a(5)=45538.
%F A287825 G.f.: (-1 - x + 4*x^2 + 3*x^3 - 3*x^4 - x^5)/(-1 + 9*x - 4*x^2 - 21*x^3 + 9*x^4 + 5*x^5).
%t A287825 LinearRecurrence[{9, -4, -21, 9, 5}, {1, 10, 82, 674, 5540, 45538}, 40]
%o A287825 (Python)
%o A287825 def a(n):
%o A287825     if n in [0, 1, 2, 3, 4, 5]:
%o A287825         return [1, 10, 82, 674, 5540, 45538][n]
%o A287825     return 9*a(n-1) - 4*a(n-2) - 21*a(n-3) + 9*a(n-4) + 5*a(n-5)
%Y A287825 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287831.
%K A287825 nonn,easy
%O A287825 0,2
%A A287825 _David Nacin_, Jun 02 2017