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 A124703 #15 Apr 30 2025 13:53:51
%S A124703 1,10,28,64,168,440,1186,3230,8896,24688,68958,193610,545958,1545190,
%T A124703 4387012,12489224,35639536,101914160,291970654,837834650,2407780858,
%U A124703 6928681418,19961961014,57573920446,166216938550,480300958390
%N A124703 Number of base 10 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124703 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C A124703 a(n) = T(n, 10) 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,..,10}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124703 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 A124703 G.f.: (1 - 36*x^2 + 96*x^3 + 42*x^4 - 336*x^5 + 175*x^6 + 216*x^7 - 126*x^8 - 32*x^9 + 9*x^10) / ((1 - 6*x + 10*x^2 - x^3 - 6*x^4 + x^5)*(1 - 4*x + 2*x^2 + 5*x^3 - 2*x^4 - x^5)) (conjectured). - _Colin Barker_, Jun 01 2017
%o A124703 (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 A124703 nonn,base
%O A124703 0,2
%A A124703 _R. H. Hardin_, Dec 28 2006