A126504 Number of base 9 n-digit numbers with adjacent digits differing by four or less.

1, 9, 61, 429, 3011, 21141, 148433, 1042167, 7317185, 51374875, 360709449, 2532586341, 17781606753, 124846894103, 876565722303, 6154478019155, 43211363078111, 303392406838867, 2130156189729353, 14956094122197975

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

Links

Table of n, a(n) for n=0..19.

Formula

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

G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 7*x - x^2 + 6*x^3 - x^5).

a(n) = 7*a(n-1) + a(n-2) - 6*a(n-3) + a(n-5) for n>5.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

Crossrefs

Cf. Base 9 differing by three or less A126477, two or less A126396, one or less A126363.

Sequence in context: A243877 A200674 A162769 * A361280 A025014 A246567

Adjacent sequences: A126501 A126502 A126503 * A126505 A126506 A126507

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved