A125421 Number of base 9 circular n-digit numbers with adjacent digits differing by 7 or less.

1, 9, 79, 681, 5987, 52649, 463087, 4073225, 35827395, 315131721, 2771845519, 24380686185, 214448408099, 1886252068073, 16591155401263, 145933007686601, 1283602149301635, 11290348248219273, 99308001030865615

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+F(7) for base>=7.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 02 2017: (Start)

G.f.: (1 - x^2 - 14*x^3) / ((1 - x)*(1 - 8*x - 7*x^2)).

a(n) = 1 + (4-sqrt(23))^n + (4+sqrt(23))^n for n>0.

a(n) = 9*a(n-1) - a(n-2) - 7*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]`-$[(i+1)mod N]`>7)+($[(i+1)mod N]`-$[i]`>7))

Crossrefs

Sequence in context: A126632 A294344 A125909 * A163445 A190979 A254598

Adjacent sequences: A125418 A125419 A125420 * A125422 A125423 A125424

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved