A126489 Number of base 21 n-digit numbers with adjacent digits differing by three or less.

1, 21, 135, 889, 5903, 39389, 263647, 1768457, 11880131, 79895207, 537729241, 3621234957, 24396753479, 164414536077, 1108268954317, 7471720473245, 50378750794147, 339712511249557, 2290882896563443, 15449485988902675

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

Table of n, a(n) for n=0..19.

Formula

G.f.: (1+9*x-84*x^2-2*x^3+321*x^4+70*x^5-178*x^6-26*x^7+13*x^8+2*x^9) / (1-12*x+33*x^2+36*x^3-125*x^4-55*x^5+70*x^6+16*x^7-5*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]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))

Crossrefs

Cf. Base 21 differing by two or less A126408, one or less A126375.

Sequence in context: A243201 A264554 A125331 * A033595 A220388 A220151

Adjacent sequences: A126486 A126487 A126488 * A126490 A126491 A126492

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved