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

0,2

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

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

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

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>1)+($[i+1]`-$[i]`>1))

Crossrefs

Sequence in context: A051876 A069174 A124717 * A342800 A320702 A006352

Adjacent sequences: A126375 A126376 A126377 * A126379 A126380 A126381

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved