A126529 Number of base 8 n-digit numbers with adjacent digits differing by five or less.

1, 8, 58, 426, 3124, 22914, 168066, 1232708, 9041498, 66316346, 486408084, 3567639634, 26167436306, 191929340708, 1407737135338, 10325278224266, 75732441613044, 555471977422754, 4074200053901346, 29882886543125508

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 8 differing by four or less A126503, three or less A126476, two or less A126395, one or less A126362.

Formula

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

G.f.: (1 + x - x^2) / (1 - 7*x - 3*x^2 + 4*x^3).

a(n) = 7*a(n-1) + 3*a(n-2) - 4*a(n-3) for n>2.

(End)