A126396 Number of base 9 n-digit numbers with adjacent digits differing by two or less.

1, 9, 39, 175, 793, 3611, 16475, 75229, 343633, 1569883, 7172423, 32769925, 149723361, 684077955, 3125520983, 14280373781, 65246447425, 298108406323, 1362045450407, 6223131628517, 28433241805745, 129910355608771

Offset: 0

Author

R. H. Hardin, Dec 28 2006

Keywords

• nonn
• base

Comments

[Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.

Crossrefs

Cf. Base 9 differing by one or less A126363.

Formula

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

G.f.: (1 + 3*x - 10*x^2 - 6*x^3 + 6*x^4 + 2*x^5) / (1 - 6*x + 5*x^2 + 8*x^3 - 4*x^4 - 2*x^5).

a(n) = 6*a(n-1) - 5*a(n-2) - 8*a(n-3) + 4*a(n-4) + 2*a(n-5) for n>5.

(End)