A126475 Number of base 7 n-digit numbers with adjacent digits differing by three or less.

1, 7, 37, 203, 1111, 6083, 33305, 182349, 998383, 5466269, 29928491, 163862147, 897165287, 4912089625, 26894291201, 147249532159, 806209189861, 4414093873755, 24167703582839, 132321131623579, 724474371929041

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 7 differing by two or less A126394, one or less A126361.

Formula

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

G.f.: (1 + 2*x - x^2 - x^3) / (1 - 5*x - 3*x^2 + 2*x^3 + x^4).

a(n) = 5*a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n>3.

(End)