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A124708
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Number of base 15 circular n-digit numbers with adjacent digits differing by 1 or less.
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0
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1, 15, 43, 99, 263, 695, 1891, 5195, 14431, 40383, 113723, 321875, 914903, 2609895, 7468147, 21427259, 61622671, 177588815, 512734699, 1482818915, 4294677703, 12455435063, 36167638627, 105140060555, 305958613855, 891185076095
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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, 15) 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,..,15}. 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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Table of n, a(n) for n=0..25.
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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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Sequence in context: A069127 A137183 A173873 * A204734 A126369 A193647
Adjacent sequences: A124705 A124706 A124707 * A124709 A124710 A124711
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KEYWORD
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nonn,base
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AUTHOR
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R. H. Hardin, Dec 28 2006
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STATUS
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approved
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