A125396 Number of base 8 circular n-digit numbers with adjacent digits differing by 6 or less.

1, 8, 62, 470, 3650, 28358, 220394, 1712894, 13312610, 103465622, 804135002, 6249738734, 48572981138, 377509300358, 2934002989322, 22803076727390, 177225555027650, 1377397345557878, 10705134749071034, 83200327316844494

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+F(6) for base>=6.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..19.

Formula

Conjectures from Colin Barker, Jun 02 2017: (Start)

G.f.: (1 - x^2 - 12*x^3) / ((1 - x)*(1 - 7*x - 6*x^2)).

a(n) = 1 + ((7-sqrt(73))/2)^n + ((7+sqrt(73))/2)^n for n>0.

a(n) = 8*a(n-1) - a(n-2) - 6*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]`-$[(i+1)mod N]`>6)+($[(i+1)mod N]`-$[i]`>6))

Crossrefs

Sequence in context: A229011 A126628 A085353 * A163444 A190975 A287815

Adjacent sequences: A125393 A125394 A125395 * A125397 A125398 A125399

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved