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 A287806 #10 May 22 2025 10:21:47
%S A287806 1,6,26,114,500,2194,9628,42252,185422,813722,3571010,15671340,
%T A287806 68773514,301811860,1324498252,5812546998,25508302906,111942925778,
%U A287806 491260382084,2155891150146,9461106209228,41519967599596,182209952129086,799626506818554,3509152727035810
%N A287806 Number of senary sequences of length n such that no two consecutive terms have distance 1.
%H A287806 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5, -2, -3).
%F A287806 For n>3, a(n) = 5*a(n-1) - 2*a(n-2) - 3*a(n-3), a(1)=6, a(2)=26, a(3)=114.
%F A287806 G.f.: (1 + x - 2*x^2 - x^3)/(1 - 5*x + 2*x^2 + 3*x^3).
%e A287806 For n=2 the a(2)=26=36-10 sequences contain every combination except these ten: 01,10,12,21,23,32,34,43,45,54.
%t A287806 LinearRecurrence[{5, -2, -3}, {1, 6, 26, 114}, 40]
%o A287806 (Python)
%o A287806 def a(n):
%o A287806 if n in [0, 1, 2, 3]:
%o A287806 return [1, 6, 26, 114][n]
%o A287806 return 5*a(n-1)-2*a(n-2)-3*a(n-3)
%Y A287806 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819.
%K A287806 nonn,easy
%O A287806 0,2
%A A287806 _David Nacin_, Jun 01 2017