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A125421
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Number of base 9 circular n-digit numbers with adjacent digits differing by 7 or less.
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0
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1, 9, 79, 681, 5987, 52649, 463087, 4073225, 35827395, 315131721, 2771845519, 24380686185, 214448408099, 1886252068073, 16591155401263, 145933007686601, 1283602149301635, 11290348248219273, 99308001030865615
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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(7) for base>=7.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 - 14*x^3) / ((1 - x)*(1 - 8*x - 7*x^2)).
a(n) = 1 + (4-sqrt(23))^n + (4+sqrt(23))^n for n>0.
a(n) = 9*a(n-1) - a(n-2) - 7*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]`-$[(i+1)mod N]`>7)+($[(i+1)mod N]`-$[i]`>7))
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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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