A126395 Number of base 8 n-digit numbers with adjacent digits differing by two or less.

1, 8, 34, 150, 668, 2986, 13362, 59816, 267802, 1199022, 5368412, 24036226, 107618586, 481846232, 2157395218, 9659418342, 43248619100, 193639305850, 866991400098, 3881825980040, 17380302665002, 77817738944382

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..21.

Formula

Conjectures from Colin Barker, Jun 01 2017: (Start)

G.f.: (1 + 3*x - 5*x^2 - 6*x^3) / (1 - 5*x + x^2 + 6*x^3).

a(n) = 5*a(n-1) - a(n-2) - 6*a(n-3) for n>3.

(End)

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 8 differing by one or less A126362.

Sequence in context: A082840 A224240 A101644 * A335749 A227330 A252934

Adjacent sequences: A126392 A126393 A126394 * A126396 A126397 A126398

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved