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

0,2

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

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

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

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))

Crossrefs

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

Sequence in context: A008663 A277984 A125334 * A222002 A240268 A231341

Adjacent sequences: A126489 A126490 A126491 * A126493 A126494 A126495

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved