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A125373
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Number of base 10 circular n-digit numbers with adjacent digits differing by 5 or less.
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2
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1, 10, 80, 580, 4660, 37960, 311378, 2559658, 21057948, 173287588, 1426133270, 11737272106, 96600478510, 795047628502, 6543462720560, 53854541701240, 443238127915788, 3647975524214452, 30023874009147704, 247105006940966092
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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(5) for base>=5.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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Table of n, a(n) for n=0..19.
Index entries for linear recurrences with constant coefficients, signature (11, -21, -19, 34, 8, -15, -1, 2).
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FORMULA
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G.f.: (1 - x - 9*x^2 - 71*x^3 + 116*x^4 + 52*x^5 - 87*x^6 - 9*x^7 + 16*x^8)/((1 + x)(1 - 3*x + x^3)(1 - 9*x + 6*x^2 + 3*x^3 - 2*x^4)). For n<4, a(n) = 5*6^n-4*5^n = A257286(n). - M. F. Hasler, May 03 2015
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MATHEMATICA
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LinearRecurrence[{11, -21, -19, 34, 8, -15, -1, 2}, {1, 10, 80, 580, 4660, 37960, 311378, 2559658, 21057948}, 30] (* Harvey P. Dale, May 14 2018 *)
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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]`-$[(i+1)mod N]`>5)+($[(i+1)mod N]`-$[i]`>5))
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CROSSREFS
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Sequence in context: A055285 A036070 A257286 * A093145 A341917 A037509
Adjacent sequences: A125370 A125371 A125372 * A125374 A125375 A125376
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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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