A126477 Number of base 9 n-digit numbers with adjacent digits differing by three or less.

1, 9, 51, 301, 1787, 10619, 63111, 375091, 2229307, 13249619, 78747531, 468026571, 2781660187, 16532466059, 98258743211, 583989138891, 3470869901227, 20628701920939, 122604233247851, 728683659684651

Offset: 0

Author

R. H. Hardin, Dec 27 2006

Keywords

• nonn
• base

Comments

[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3.

Crossrefs

Cf. Base 9 differing by two or less A126396, one or less A126363.

Formula

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

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

a(n) = 7*a(n-1) - 6*a(n-2) - 2*a(n-3) + 2*a(n-4) for n>4.

(End)