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 A124702 #16 Apr 30 2025 13:53:32
%S A124702 1,9,25,57,149,389,1045,2837,7789,21549,60005,167957,472169,1332249,
%T A124702 3770785,10701617,30442909,86779229,247817845,708837797,2030401509,
%U A124702 5823331109,16720830525,48060737357,138268935049,398126270889
%N A124702 Number of base 9 circular n-digit numbers with adjacent digits differing by 1 or less.
%C A124702 [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
%C A124702 a(n) = T(n, 9) 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,..,9}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%H A124702 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 A124702 G.f.: (1 - 28*x^2 + 56*x^3 + 63*x^4 - 196*x^5 + 30*x^6 + 108*x^7 - 21*x^8 - 8*x^9) / ((1 - x)*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 4*x + x^2 + 6*x^3 + x^4)) (conjectured). - _Colin Barker_, Jun 02 2017
%o A124702 (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 A124702 nonn,base
%O A124702 0,2
%A A124702 _R. H. Hardin_, Dec 28 2006