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 A287815 #11 May 22 2025 10:21:47
%S A287815 1,8,62,482,3746,29114,226274,1758602,13667858,106226618,825593474,
%T A287815 6416514026,49869159026,387583197338,3012297335522,23411580532682,
%U A287815 181954847741906,1414153417389434,10990803008177474,85420541561578922,663888608980117298,5159743512230294618
%N A287815 Number of octonary sequences of length n such that no two consecutive terms have distance 7.
%H A287815 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7, 6).
%F A287815 a(n) = 7*a(n-1) + 6*a(n-2), a(0)=1, a(1)=8.
%F A287815 G.f.: (-1 - x)/(-1 + 7 x + 6 x^2).
%F A287815 a(n) = A015564(n)+A015564(n+1). - _R. J. Mathar_, Oct 20 2019
%e A287815 For n=2 the a(2) = 64 - 2 = 62 sequences contain every combination except these two: 07,70.
%t A287815 LinearRecurrence[{7, 6}, {1, 8}, 40]
%o A287815 (Python)
%o A287815 def a(n):
%o A287815 if n in [0, 1]:
%o A287815 return [1, 8][n]
%o A287815 return 7*a(n-1)+6*a(n-2)
%Y A287815 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819.
%K A287815 nonn,easy
%O A287815 0,2
%A A287815 _David Nacin_, Jun 02 2017