A126503 Number of base 8 n-digit numbers with adjacent digits differing by four or less.

1, 8, 52, 348, 2322, 15500, 103462, 690610, 4609826, 30770620, 205394096, 1371006978, 9151480836, 61086196378, 407750773322, 2721739165358, 18167627307952, 121269034961780, 809471627267722, 5403228578160660

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Links

Table of n, a(n) for n=0..19.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)

G.f.: (1 + 2*x - x^2 - x^3) / (1 - 6*x - 5*x^2 + 3*x^3 + 2*x^4).

a(n) = 6*a(n-1) + 5*a(n-2) - 3*a(n-3) - 2*a(n-4) for n>3.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

Crossrefs

Cf. Base 8 differing by three or less A126476, two or less A126395, one or less A126362.

Sequence in context: A006631 A205218 A287813 * A155590 A130153 A359126

Adjacent sequences: A126500 A126501 A126502 * A126504 A126505 A126506

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved