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A125445
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Number of base 10 circular n-digit numbers with adjacent digits differing by 8 or less.
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0
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1, 10, 98, 946, 9282, 91090, 894050, 8775154, 86128770, 845360146, 8297271458, 81438324274, 799323090114, 7845414405202, 77003314367714, 755793144551026, 7418164815900930, 72809828499516562, 714633775022856482
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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(8) for base>=8.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 - 16*x^3) / ((1 - x)*(1 - 9*x - 8*x^2)).
a(n) = 1 + ((9-sqrt(113))/2)^n + ((9+sqrt(113))/2)^n for n>0.
a(n) = 10*a(n-1) - a(n-2) - 8*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]`-$[(i+1)mod N]`>8)+($[(i+1)mod N]`-$[i]`>8))
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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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