A126378 Number of base 24 n-digit numbers with adjacent digits differing by one or less.

1, 24, 70, 206, 608, 1798, 5324, 15780, 46806, 138918, 412508, 1225432, 3641690, 10825628, 32190154, 95741294, 284820048, 847475910, 2522096172, 7507000776, 22347852666, 66537181776, 198128815230, 590039959434, 1757365514652

Offset: 0

Author

R. H. Hardin, Dec 26 2006

Keywords

• nonn
• base

Comments

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

Links

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

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, add(
     `if`(i=0 or abs(i-j)<2, 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.: -(7*x^12 +92*x^11 -206*x^10 -680*x^9 +1145*x^8 +946*x^7 -2100*x^6 +318*x^5 +1050*x^4 -725*x^3 +176*x^2 -11*x -1) / ((x^2 -3*x +1)*(x^10 +15*x^9 +10*x^8 -65*x^7 -10*x^6 +97*x^5 -35*x^4 -40*x^3 +35*x^2 -10*x +1)). - Alois P. Heinz, Sep 25 2015