A126374 Number of base 20 n-digit numbers with adjacent digits differing by one or less.

1, 20, 58, 170, 500, 1474, 4352, 12864, 38058, 112674, 333776, 989236, 2933102, 8699864, 25812862, 76609418, 227424420, 675289026, 2005535520, 5957318820, 17698806798, 52590044172, 156287402420, 464515721050, 1380792800096

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+9*x-117*x^2+356*x^3-266*x^4-399*x^5+546*x^6+82*x^7-216*x^8+x^9+12*x^10) / ((1-2*x)*(1-4*x+3*x^2+x^3)*(1-5*x+4*x^2+8*x^3-5*x^4-3*x^5+x^6)) (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: A104100 A069132 A124713 * A229536 A220013 A220046

Adjacent sequences: A126371 A126372 A126373 * A126375 A126376 A126377

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved