A126476 Number of base 8 n-digit numbers with adjacent digits differing by three or less.

1, 8, 44, 252, 1446, 8300, 47642, 273466, 1569700, 9010108, 51718192, 296863410, 1704001644, 9781001986, 56143138234, 322262685896, 1849793972828, 10617852738356, 60946677537854, 349835093256180, 2008060117756986

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 8 differing by two or less A126395, one or less A126362.

Formula

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

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

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

(End)