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 A124701 #16 Apr 30 2025 13:53:06
%S A124701 1,8,22,50,130,338,904,2444,6682,18410,51052,142304,398380,1119308,
%T A124701 3154558,8914010,25246282,71644298,203665054,579841286,1653025900,
%U A124701 4718011460,13479908926,38548802570,110327691316,315985475588
%N A124701 Number of base 8 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124701 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C A124701 a(n) = T(n, 8) 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,..,8}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124701 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 A124701 G.f.: (1 - 21*x^2 + 28*x^3 + 60*x^4 - 96*x^5 - 15*x^6 + 36*x^7) / ((1 - 2*x)*(1 - 3*x + x^3)*(1 - 3*x + 3*x^3)) (conjectured). - _Colin Barker_, Jun 03 2017
%o A124701 (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 A124701 nonn,base
%O A124701 0,2
%A A124701 _R. H. Hardin_, Dec 28 2006