A126476 Number of base 8 n-digit numbers with adjacent digits differing by three or less.

1, 8, 44, 252, 1446, 8300, 47642, 273466, 1569700, 9010108, 51718192, 296863410, 1704001644, 9781001986, 56143138234, 322262685896, 1849793972828, 10617852738356, 60946677537854, 349835093256180, 2008060117756986

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..20.

Formula

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

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

a(n) = 6*a(n-1) - a(n-2) - 3*a(n-3) + 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 8 differing by two or less A126395, one or less A126362.

Sequence in context: A322498 A147828 A155604 * A220629 A210118 A112908

Adjacent sequences: A126473 A126474 A126475 * A126477 A126478 A126479

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved