A126502 Number of base 7 n-digit numbers with adjacent digits differing by four or less.

1, 7, 43, 269, 1679, 10483, 65449, 408623, 2551187, 15928021, 99444631, 620870267, 3876326801, 24201367447, 151098247483, 943363239389, 5889771828959, 36772062710083, 229581830200249, 1433365791134783

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

Comments

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Crossrefs

Cf. Base 7 differing by three or less A126475, two or less A126394, one or less A126361.

Formula

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

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

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

(End)