A126372 Number of base 18 n-digit numbers with adjacent digits differing by one or less.

1, 18, 52, 152, 446, 1312, 3866, 11406, 33684, 99552, 294410, 871138, 2578808, 7636982, 22624216, 67043480, 198726606, 589195584, 1747255194, 5182477842, 15374283866, 45616475418, 135366696658, 401753608184, 1192506493748

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

Table of n, a(n) for n=0..24.

Formula

G.f.: (1+8*x-92*x^2+231*x^3-91*x^4-281*x^5+202*x^6+87*x^7-51*x^8-5*x^9) / (1-10*x+36*x^2-49*x^3-7*x^4+69*x^5-30*x^6-21*x^7+9*x^8+x^9) (conjectured). - Colin Barker, Jul 18 2017

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: A069130 A299071 A124711 * A334645 A133356 A367345

Adjacent sequences: A126369 A126370 A126371 * A126373 A126374 A126375

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved