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%I #9 May 31 2017 13:17:34
%S 1,10,58,350,2130,12990,79258,483646,2951370,18010366,109906170,
%T 670689902,4092809194,24975905246,152412637946,930080892110,
%U 5675713495690,34635399953406,211358612597658,1289792038765742
%N Number of base 10 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_, May 31 2017: (Start)
%F G.f.: (1 + 3*x - 8*x^2 - 6*x^3 + 6*x^4) / (1 - 7*x + 4*x^2 + 10*x^3 - 6*x^4).
%F a(n) = 7*a(n-1) - 4*a(n-2) - 10*a(n-3) + 6*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 10 differing by two or less A126397, one or less A126364.
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 27 2006
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