This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287816 #9 May 22 2025 10:21:47
%S A287816 1,9,65,471,3413,24733,179233,1298853,9412437,68209395,494295113,
%T A287816 3582023557,25957960001,188110345129,1363185009337,9878634630295,
%U A287816 71587804656589,518777540353453,3759441118026705,27243657291488469,197427447142906157,1430703538380753875
%N A287816 Number of nonary sequences of length n such that no two consecutive terms have distance 1.
%H A287816 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (9, -11, -15, 19, 1).
%F A287816 a(n) = 9*a(n-1) - 11*a(n-2) - 15*a(n-3) + 19*a(n-4) + a(n-5), a(0)=1, a(1)=9, a(2)=65, a(3)=471, a(4)=3413.
%F A287816 G.f: (-1 + 5 x^2 - 5 x^4)/(-1 + 9 x - 11 x^2 - 15 x^3 + 19 x^4 + x^5).
%e A287816 For n=2 the a(2) = 81 - 16 = 65 sequences contain every combination except these sixteen: 01,10,12,21,23,32,34,43,45,54,56,65,67,76,78,87.
%t A287816 LinearRecurrence[{9, -11, -15, 19, 1}, {1, 9, 65 , 471, 3413}, 40]
%o A287816 (Python)
%o A287816 def a(n):
%o A287816 if n in [0, 1, 2, 3, 4]:
%o A287816 return [1, 9, 65 , 471, 3413][n]
%o A287816 return 9*a(n-1)-11*a(n-2)-15*a(n-3)+19*a(n-4)+a(n-5)
%Y A287816 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819.
%K A287816 nonn,easy
%O A287816 0,2
%A A287816 _David Nacin_, Jun 02 2017