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

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

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.

Crossrefs

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

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)