A126395 Number of base 8 n-digit numbers with adjacent digits differing by two or less.

1, 8, 34, 150, 668, 2986, 13362, 59816, 267802, 1199022, 5368412, 24036226, 107618586, 481846232, 2157395218, 9659418342, 43248619100, 193639305850, 866991400098, 3881825980040, 17380302665002, 77817738944382

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

Comments

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

Crossrefs

Cf. Base 8 differing by one or less A126362.

Formula

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

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

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

(End)