A126502 - OEIS

%I #11 Jun 01 2017 12:06:20

%S 1,7,43,269,1679,10483,65449,408623,2551187,15928021,99444631,

%T 620870267,3876326801,24201367447,151098247483,943363239389,

%U 5889771828959,36772062710083,229581830200249,1433365791134783

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

%C [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.

%F Conjectures from _Colin Barker_, Jun 01 2017: (Start)

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

%F a(n) = 6*a(n-1) + 2*a(n-2) - 3*a(n-3) for n>2.

%F (End)

%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

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

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006