A126375 Number of base 21 n-digit numbers with adjacent digits differing by one or less.

1, 21, 61, 179, 527, 1555, 4595, 13593, 40245, 119235, 353459, 1048285, 3110249, 9231305, 27407185, 81392387, 241773327, 718335747, 2134675683, 6344739309, 18861068265, 56076828573, 166747755621, 495896780609, 1474935978225

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+10*x-126*x^2+366*x^3-166*x^4-700*x^5+679*x^6+426*x^7-466*x^8-104*x^9+73*x^10+6*x^11) / ((1-x)*(1-10*x+34*x^2-32*x^3-54*x^4+100*x^5+23*x^6-76*x^7-10*x^8+12*x^9+x^10)) (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: A325319 A069133 A124714 * A146468 A081302 A058100

Adjacent sequences: A126372 A126373 A126374 * A126376 A126377 A126378

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved