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A125396
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Number of base 8 circular n-digit numbers with adjacent digits differing by 6 or less.
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0
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1, 8, 62, 470, 3650, 28358, 220394, 1712894, 13312610, 103465622, 804135002, 6249738734, 48572981138, 377509300358, 2934002989322, 22803076727390, 177225555027650, 1377397345557878, 10705134749071034, 83200327316844494
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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)+F(6) for base>=6.int(n/2)+1 and F(d) is the largest coefficient in (1+x+...+x^(2d))^n
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LINKS
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FORMULA
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G.f.: (1 - x^2 - 12*x^3) / ((1 - x)*(1 - 7*x - 6*x^2)).
a(n) = 1 + ((7-sqrt(73))/2)^n + ((7+sqrt(73))/2)^n for n>0.
a(n) = 8*a(n-1) - a(n-2) - 6*a(n-3) for n>3.
(End)
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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]`-$[(i+1)mod N]`>6)+($[(i+1)mod N]`-$[i]`>6))
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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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