A125370 Number of base 7 circular n-digit numbers with adjacent digits differing by 5 or less.

1, 7, 47, 307, 2067, 13927, 93887, 632947, 4267107, 28767367, 193939727, 1307475187, 8814549747, 59424674407, 400620795167, 2700848143027, 18208192833987, 122753397719047, 827561350484207, 5579135091500467

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+F(5) for base>=5.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 - 10*x^3) / ((1 - x)*(1 - 6*x - 5*x^2)).

a(n) = 1 + (3-sqrt(14))^n + (3+sqrt(14))^n for n>0.

a(n) = 7*a(n-1) - a(n-2) - 5*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]`-$[(i+1)mod N]`>5)+($[(i+1)mod N]`-$[i]`>5))

Crossrefs

Sequence in context: A229010 A126635 A085352 * A163346 A186446 A244830

Adjacent sequences: A125367 A125368 A125369 * A125371 A125372 A125373

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved