A126529 Number of base 8 n-digit numbers with adjacent digits differing by five or less.

1, 8, 58, 426, 3124, 22914, 168066, 1232708, 9041498, 66316346, 486408084, 3567639634, 26167436306, 191929340708, 1407737135338, 10325278224266, 75732441613044, 555471977422754, 4074200053901346, 29882886543125508

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

Links

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

Formula

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

G.f.: (1 + x - x^2) / (1 - 7*x - 3*x^2 + 4*x^3).

a(n) = 7*a(n-1) + 3*a(n-2) - 4*a(n-3) for n>2.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))

Crossrefs

Cf. Base 8 differing by four or less A126503, three or less A126476, two or less A126395, one or less A126362.

Sequence in context: A178730 A190978 A254663 * A039759 A244939 A047867

Adjacent sequences: A126526 A126527 A126528 * A126530 A126531 A126532

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved