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 A124704 #16 Apr 30 2025 13:54:13
%S A124704 1,11,31,71,187,491,1327,3623,10003,27827,77911,219263,619747,1758131,
%T A124704 5003239,14276831,40836163,117049091,336123463,966831503,2785160227,
%U A124704 8034032147,23203096519,67087148063,194165268355,562477731491
%N A124704 Number of base 11 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124704 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C A124704 a(n) = T(n, 11) 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,..,11}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124704 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 A124704 G.f.: (1 - 45*x^2 + 150*x^3 - 18*x^4 - 504*x^5 + 490*x^6 + 300*x^7 - 420*x^8 - 32*x^9 + 72*x^10) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 4*x + 2*x^2 + 4*x^3 - 2*x^4)) (conjectured). - _Colin Barker_, Jun 03 2017
%o A124704 (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 A124704 nonn,base
%O A124704 0,2
%A A124704 _R. H. Hardin_, Dec 28 2006