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%I #9 Jun 01 2017 12:06:00
%S 1,7,37,203,1111,6083,33305,182349,998383,5466269,29928491,163862147,
%T 897165287,4912089625,26894291201,147249532159,806209189861,
%U 4414093873755,24167703582839,132321131623579,724474371929041
%N Number of base 7 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 - x^2 - x^3) / (1 - 5*x - 3*x^2 + 2*x^3 + x^4).
%F a(n) = 5*a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n>3.
%F (End)
%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>3)+($[i+1]`-$[i]`>3))
%Y Cf. Base 7 differing by two or less A126394, one or less A126361.
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 27 2006
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