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 A124700 #15 Apr 30 2025 13:52:40
%S A124700 1,7,19,43,111,287,763,2051,5575,15271,42099,116651,324591,906367,
%T A124700 2538331,7126403,20049671,56509639,159514963,450865067,1275778031,
%U A124700 3613401695,10242581819,29053799555,82461727687,234163952487
%N A124700 Number of base 7 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124700 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1.
%C A124700 a(n) = T(n, 7) 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,..,7}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124700 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 A124700 G.f.: (1 - 2*x)*(1 + 2*x - 11*x^2 - 12*x^3 + 21*x^4 + 6*x^5 - 3*x^6) / ((1 - x)*(1 - 2*x - x^2)*(1 - 4*x + 2*x^2 + 4*x^3 - x^4)) (conjectured). - _Colin Barker_, Jun 03 2017
%o A124700 (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 A124700 nonn,base
%O A124700 0,2
%A A124700 _R. H. Hardin_, Dec 28 2006