A125445 Number of base 10 circular n-digit numbers with adjacent digits differing by 8 or less.

1, 10, 98, 946, 9282, 91090, 894050, 8775154, 86128770, 845360146, 8297271458, 81438324274, 799323090114, 7845414405202, 77003314367714, 755793144551026, 7418164815900930, 72809828499516562, 714633775022856482

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