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A124718
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Number of base 25 circular n-digit numbers with adjacent digits differing by 1 or less.
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0
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1, 25, 73, 169, 453, 1205, 3301, 9125, 25501, 71773, 203253, 578405, 1652793, 4739305, 13630417, 39303329, 113588941, 328938125, 954262789, 2772787445, 8068471393, 23508942353, 68578993897, 200272341785, 585441977665
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OFFSET
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0,2
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COMMENTS
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[Empirical] a(base,n)=a(base-1,n)+A002426(n+1) for base>=1.int(n/2)+1
a(n) = T(n, 25) 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,..,25}. See theorem 3.3 in Knopfmacher and others, reference in A124696. - Peter Luschny, Aug 13 2012
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LINKS
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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