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 A287837 #10 May 22 2025 10:21:46
%S A287837 1,11,113,1163,11969,123179,1267697,13046507,134268161,1381821131,
%T A287837 14221015793,146355621323,1506219260609,15501259470059,
%U A287837 159531252482417,1641816303234347,16896756789790721,173893016807610251,1789620438445474673,18417883434877577483
%N A287837 Number of words over the alphabet {0,1,...,10} such that no two consecutive terms have distance 7.
%C A287837 In general, the number of sequences on {0,1,...,10} such that no two consecutive terms have distance 6+k for k in {0,1,2,3,4} has generating function (-1 - x)/(-1 + 10*x + (2*k+1)*x^2).
%H A287837 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,3).
%F A287837 For n>2, a(n) = 10*a(n-1) + 3*a(n-2), a(0)=1, a(1)=11, a(2)=113.
%F A287837 G.f.: (-1 - x)/(-1 + 10*x + 3*x^2).
%F A287837 a(n) = A015588(n)+A015588(n+1). - _R. J. Mathar_, Oct 20 2019
%t A287837 LinearRecurrence[{10, 3}, {1, 11, 113}, 20]
%o A287837 (Python)
%o A287837 def a(n):
%o A287837 if n in [0,1,2]:
%o A287837 return [1, 11, 113][n]
%o A287837 return 10*a(n-1) + 3*a(n-2)
%Y A287837 Cf. A040000, A003945, A083318, A078057, A003946, A126358, A003946, A055099, A003947, A015448, A126473. A287804-A287819. A287825-A287839.
%K A287837 nonn,easy
%O A287837 0,2
%A A287837 _David Nacin_, Jun 07 2017