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A125445 Number of base 10 circular n-digit numbers with adjacent digits differing by 8 or less. 0
1, 10, 98, 946, 9282, 91090, 894050, 8775154, 86128770, 845360146, 8297271458, 81438324274, 799323090114, 7845414405202, 77003314367714, 755793144551026, 7418164815900930, 72809828499516562, 714633775022856482 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

[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

LINKS

Table of n, a(n) for n=0..18.

FORMULA

Conjectures from Colin Barker, Jun 01 2017: (Start)

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)

PROG

(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))

CROSSREFS

Sequence in context: A125946 A158513 A125880 * A163446 A190869 A254599

Adjacent sequences:  A125442 A125443 A125444 * A125446 A125447 A125448

KEYWORD

nonn,base

AUTHOR

R. H. Hardin, Dec 28 2006

STATUS

approved

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Last modified June 29 23:00 EDT 2022. Contains 354913 sequences. (Running on oeis4.)