A125468 Number of base 11 circular n-digit numbers with adjacent digits differing by 9 or less.

1, 11, 119, 1271, 13763, 149051, 1614359, 17485031, 189379523, 2051160491, 22216020599, 240620650391, 2606150689283, 28227092746331, 305726283666839, 3311306671385351, 35864603266855043, 388447792711018571

Offset

0,2

Comments

[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.

Links

Table of n, a(n) for n=0..17.

Formula

Conjectures from Colin Barker, Jun 04 2017: (Start)

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)

Prog

(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))

Crossrefs

Sequence in context: A289344 A240392 A044724 * A163447 A254600 A354906

Adjacent sequences: A125465 A125466 A125467 * A125469 A125470 A125471

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved