A126530 Number of base 9 n-digit numbers with adjacent digits differing by five or less.

1, 9, 69, 541, 4231, 33101, 258953, 2025831, 15848391, 123984439, 969949627, 7588067405, 59362636295, 464403174075, 3633098554089, 28422297349753, 222352070721709, 1739494972761653, 13608340819322255, 106460175369651261

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

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 + x)*(1 - 8*x + x^2 + 3*x^3)).

a(n) = 7*a(n-1) + 7*a(n-2) - 4*a(n-3) - 3*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]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))

Crossrefs

Cf. Base 9 differing by four or less A126504, three or less A126477, two or less A126396, one or less A126363.

Sequence in context: A299915 A287818 A297222 * A351810 A152273 A217452

Adjacent sequences: A126527 A126528 A126529 * A126531 A126532 A126533

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved