A126395 - OEIS

%I #9 Jun 01 2017 12:05:44

%S 1,8,34,150,668,2986,13362,59816,267802,1199022,5368412,24036226,

%T 107618586,481846232,2157395218,9659418342,43248619100,193639305850,

%U 866991400098,3881825980040,17380302665002,77817738944382

%N Number of base 8 n-digit numbers with adjacent digits differing by two or less.

%C [Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.

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

%F G.f.: (1 + 3*x - 5*x^2 - 6*x^3) / (1 - 5*x + x^2 + 6*x^3).

%F a(n) = 5*a(n-1) - a(n-2) - 6*a(n-3) for n>3.

%F (End)

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

%Y Cf. Base 8 differing by one or less A126362.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006