A126502 Number of base 7 n-digit numbers with adjacent digits differing by four or less.

1, 7, 43, 269, 1679, 10483, 65449, 408623, 2551187, 15928021, 99444631, 620870267, 3876326801, 24201367447, 151098247483, 943363239389, 5889771828959, 36772062710083, 229581830200249, 1433365791134783

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 - x^2) / (1 - 6*x - 2*x^2 + 3*x^3).

a(n) = 6*a(n-1) + 2*a(n-2) - 3*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]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

Crossrefs

Cf. Base 7 differing by three or less A126475, two or less A126394, one or less A126361.

Sequence in context: A277670 A015451 A194779 * A286911 A343351 A277188

Adjacent sequences: A126499 A126500 A126501 * A126503 A126504 A126505

Keyword

nonn,base

Author

R. H. Hardin, Dec 28 2006

Status

approved