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%I #9 Jun 01 2017 12:06:14
%S 1,9,51,301,1787,10619,63111,375091,2229307,13249619,78747531,
%T 468026571,2781660187,16532466059,98258743211,583989138891,
%U 3470869901227,20628701920939,122604233247851,728683659684651
%N Number of base 9 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 + 2*x - 6*x^2 + 2*x^4) / ((1 - x)*(1 - 6*x + 2*x^3)).
%F a(n) = 7*a(n-1) - 6*a(n-2) - 2*a(n-3) + 2*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 9 differing by two or less A126396, one or less A126363.
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 27 2006
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