A126403 Number of base 16 n-digit numbers with adjacent digits differing by two or less.

1, 16, 74, 350, 1668, 7986, 38348, 184524, 889230, 4290030, 20714382, 100083072, 483793208, 2339478320, 11316186924, 54748710158, 264922095330, 1282082867386, 6205185792886, 30034782040334, 145384379570694

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.

Links

Table of n, a(n) for n=0..20.

Formula

G.f.: (1+7*x-51*x^2+4*x^3+131*x^4+10*x^5-61*x^6-2*x^7+3*x^8) / (1-9*x+19*x^2+16*x^3-49*x^4-14*x^5+23*x^6+2*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]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))

Crossrefs

Cf. Base 16 differing by one or less A126370.

Sequence in context: A058333 A232337 A124894 * A197873 A232863 A200786

Adjacent sequences: A126400 A126401 A126402 * A126404 A126405 A126406

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved