|
%I #9 Jun 01 2017 12:06:07
%S 1,8,44,252,1446,8300,47642,273466,1569700,9010108,51718192,296863410,
%T 1704001644,9781001986,56143138234,322262685896,1849793972828,
%U 10617852738356,60946677537854,349835093256180,2008060117756986
%N Number of base 8 n-digit numbers with adjacent digits differing by three or less.
%C [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.
%F Conjectures from _Colin Barker_, Jun 01 2017: (Start)
%F G.f.: (1 - x)*(1 + 3*x - x^3) / (1 - 6*x + x^2 + 3*x^3 - x^4).
%F a(n) = 6*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4) for n>4.
%F (End)
%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))
%Y Cf. Base 8 differing by two or less A126395, one or less A126362.
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 27 2006
|
