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A125468
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Number of base 11 circular n-digit numbers with adjacent digits differing by 9 or less.
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0
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1, 11, 119, 1271, 13763, 149051, 1614359, 17485031, 189379523, 2051160491, 22216020599, 240620650391, 2606150689283, 28227092746331, 305726283666839, 3311306671385351, 35864603266855043, 388447792711018571
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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(9) for base>=9.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 - 18*x^3) / ((1 - x)*(1 - 10*x - 9*x^2)).
a(n) = 1 + (5-sqrt(34))^n + (5+sqrt(34))^n for n>0.
a(n) = 11*a(n-1) - a(n-2) - 9*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]`-$[(i+1)mod N]`>9)+($[(i+1)mod N]`-$[i]`>9))
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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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