The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #14 Jun 04 2017 06:46:53
%S 1,5,13,29,73,185,481,1265,3361,8993,24193,65345,177025,480641,
%T 1307137,3559169,9699841,26452481,72173569,196989953,537802753,
%U 1468536833,4010582017,10954043393,29920862209,81733033985,223274237953
%N Number of base 5 circular n-digit numbers with adjacent digits differing by 1 or less.
%C [Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1.
%C a(n) = T(n, 5) 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,..,5}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%F Conjectures from _Colin Barker_, Jun 04 2017: (Start)
%F G.f.: (1 - 6*x^2 - 4*x^3 + 12*x^4) / ((1 - x)*(1 - 2*x)*(1 - 2*x - 2*x^2)).
%F a(n) = 5*a(n-1) - 6*a(n-2) - 2*a(n-3) + 4*a(n-4) for n>4.
%F (End)
%o (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 nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 28 2006