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%I #16 Jul 18 2017 01:46:17
%S 1,12,34,78,206,542,1468,4016,11110,30966,86864,244916,693536,1971072,
%T 5619466,16064438,46032790,132184022,380276272,1095828356,3162539596,
%U 9139382876,26444232046,76600376186,222113604712,644654567192
%N Number of base 12 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, 12) 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,..,12}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - _Peter Luschny_, Aug 13 2012
%F G.f.: (1 - 55*x^2 + 220*x^3 - 135*x^4 - 672*x^5 + 1050*x^6 + 216*x^7 - 1015*x^8 + 160*x^9 + 270*x^10 - 40*x^11 - 11*x^12) / ((1 - 5*x + 5*x^2 + 6*x^3 - 7*x^4 - 2*x^5 + x^6)*(1 - 7*x + 15*x^2 - 6*x^3 - 11*x^4 + 6*x^5 + x^6)) (conjectured). - _Colin Barker_, Jul 17 2017
%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
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