A126475 Number of base 7 n-digit numbers with adjacent digits differing by three or less.

1, 7, 37, 203, 1111, 6083, 33305, 182349, 998383, 5466269, 29928491, 163862147, 897165287, 4912089625, 26894291201, 147249532159, 806209189861, 4414093873755, 24167703582839, 132321131623579, 724474371929041

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 + 2*x - x^2 - x^3) / (1 - 5*x - 3*x^2 + 2*x^3 + x^4).

a(n) = 5*a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n>3.

(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 7 differing by two or less A126394, one or less A126361.

Sequence in context: A002683 A319013 A362247 * A274674 A255672 A077239

Adjacent sequences: A126472 A126473 A126474 * A126476 A126477 A126478

Keyword

nonn,base

Author

R. H. Hardin, Dec 27 2006

Status

approved