A126478 Number of base 10 n-digit numbers with adjacent digits differing by three or less.

1, 10, 58, 350, 2130, 12990, 79258, 483646, 2951370, 18010366, 109906170, 670689902, 4092809194, 24975905246, 152412637946, 930080892110, 5675713495690, 34635399953406, 211358612597658, 1289792038765742

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 10 differing by two or less A126397, one or less A126364.

Formula

Conjectures from Colin Barker, May 31 2017: (Start)

G.f.: (1 + 3*x - 8*x^2 - 6*x^3 + 6*x^4) / (1 - 7*x + 4*x^2 + 10*x^3 - 6*x^4).

a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 6*a(n-4) for n>4.

(End)