A126477 Number of base 9 n-digit numbers with adjacent digits differing by three or less.

1, 9, 51, 301, 1787, 10619, 63111, 375091, 2229307, 13249619, 78747531, 468026571, 2781660187, 16532466059, 98258743211, 583989138891, 3470869901227, 20628701920939, 122604233247851, 728683659684651

Offset

0,2

Comments

[Empirical] a(base,n)=a(base-1,n)+7^(n-1) for base>=3n-2; a(base,n)=a(base-1,n)+7^(n-1)-2 when base=3n-3.

Links

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

Formula

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

G.f.: (1 + 2*x - 6*x^2 + 2*x^4) / ((1 - x)*(1 - 6*x + 2*x^3)).

a(n) = 7*a(n-1) - 6*a(n-2) - 2*a(n-3) + 2*a(n-4) for n>4.

(End)

Prog

(S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))

Crossrefs

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

Sequence in context: A080621 A027218 A155617 * A275861 A210054 A272393

Adjacent sequences: A126474 A126475 A126476 * A126478 A126479 A126480

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved