A126368 Number of base 14 n-digit numbers with adjacent digits differing by one or less.

1, 14, 40, 116, 338, 988, 2894, 8490, 24936, 73308, 215678, 634942, 1870220, 5511218, 16246924, 47911604, 141330980, 417008740, 1230695000, 3632799810, 10725265920, 31669512054, 93526269170, 276234529396, 815959178108

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+6*x-51*x^2+75*x^3+25*x^4-72*x^5+x^6+8*x^7) / ((1-2*x)*(1-3*x+x^2)*(1-3*x-x^2+3*x^3+x^4)) (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: A101740 A069126 A124707 * A125816 A105869 A216298

Adjacent sequences: A126365 A126366 A126367 * A126369 A126370 A126371

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved