A126529 - OEIS

%I #11 Jun 01 2017 12:06:40

%S 1,8,58,426,3124,22914,168066,1232708,9041498,66316346,486408084,

%T 3567639634,26167436306,191929340708,1407737135338,10325278224266,

%U 75732441613044,555471977422754,4074200053901346,29882886543125508

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

%C [Empirical] a(base,n)=a(base-1,n)+11^(n-1) for base>=5n-4; a(base,n)=a(base-1,n)+11^(n-1)-2 when base=5n-5.

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

%F G.f.: (1 + x - x^2) / (1 - 7*x - 3*x^2 + 4*x^3).

%F a(n) = 7*a(n-1) + 3*a(n-2) - 4*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]`-$[i+1]`>5)+($[i+1]`-$[i]`>5))

%Y Cf. Base 8 differing by four or less A126503, three or less A126476, two or less A126395, one or less A126362.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006