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 A124698 #16 Apr 30 2025 13:50:53
%S A124698 1,5,13,29,73,185,481,1265,3361,8993,24193,65345,177025,480641,
%T A124698 1307137,3559169,9699841,26452481,72173569,196989953,537802753,
%U A124698 1468536833,4010582017,10954043393,29920862209,81733033985,223274237953
%N A124698 Number of base 5 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124698 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1.
%C A124698 a(n) = T(n, 5) where T(n, k) = Sum_{j=1..k} (1+2*cos(j*Pi/(k+1)))^n. These are the number of smooth cyclic words of length n over the alphabet {1,2,..,5}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124698 OEIS Wiki, <a href="/wiki/Number_of_base_k_circular_n-digit_numbers_with_adjacent_digits_differing_by_d_or_less">Number of base k circular n-digit numbers with adjacent digits differing by d or less</a>
%F A124698 Conjectures from _Colin Barker_, Jun 04 2017: (Start)
%F A124698 G.f.: (1 - 6*x^2 - 4*x^3 + 12*x^4) / ((1 - x)*(1 - 2*x)*(1 - 2*x - 2*x^2)).
%F A124698 a(n) = 5*a(n-1) - 6*a(n-2) - 2*a(n-3) + 4*a(n-4) for n>4.
%F A124698 (End)
%o A124698 (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-1](($[i]`-$[(i+1)mod N]`>1)+($[(i+1)mod N]`-$[i]`>1))
%K A124698 nonn,base
%O A124698 0,2
%A A124698 _R. H. Hardin_, Dec 28 2006