A126370 Number of base 16 n-digit numbers with adjacent digits differing by one or less.

1, 16, 46, 134, 392, 1150, 3380, 9948, 29310, 86430, 255044, 753040, 2224514, 6574100, 19435570, 57477542, 170028792, 503102142, 1488974870, 4407636908, 13049761478, 38642911632, 114446028208, 338991739166, 1004221622462

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+7*x-70*x^2+139*x^3-5*x^4-161*x^5+48*x^6+39*x^7-5*x^8) / (1-9*x+28*x^2-29*x^3-15*x^4+39*x^5-6*x^6-9*x^7+x^8) (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: A124709 A244094 A235549 * A133345 A253231 A253350

Adjacent sequences: A126367 A126368 A126369 * A126371 A126372 A126373

Keyword

nonn,base

Author

R. H. Hardin, Dec 26 2006

Status

approved