A126492 Number of base 24 n-digit numbers with adjacent digits differing by three or less.

1, 24, 156, 1036, 6932, 46592, 314068, 2121404, 14350760, 97189500, 658783572, 4468484736, 30325445672, 205889162656, 1398299571460, 9498979946468, 64541625486340, 438601729211104, 2980942930020288, 20261817487044168

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. Base 24 differing by two or less A126411, one or less A126378.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, add(
     `if`(i=0 or abs(i-j)<4, b(n-1, j), 0), j=1..24))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 25 2015

Formula

G.f.: -(36*x^11 -104*x^10 -272*x^9 +557*x^8 +624*x^7 -998*x^6 -524*x^5 +660*x^4 +134*x^3 -127*x^2 +10*x +1) / (12*x^11 -40*x^10 -80*x^9 +223*x^8 +156*x^7 -410*x^6 -88*x^5 +276*x^4 -10*x^3 -53*x^2 +14*x -1). - Alois P. Heinz, Sep 25 2015