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%I #10 May 31 2017 13:18:20
%S 1,10,44,200,918,4236,19598,90790,420870,1951636,9051480,41983154,
%T 194736668,903293618,4190003458,19435777562,90155141564,418195731384,
%U 1939853565942,8998257693932,41739569773726,193614349514214
%N Number of base 10 n-digit numbers with adjacent digits differing by two or less.
%C [Empirical] a(base,n)=a(base-1,n)+5^(n-1) for base>=2n-1; a(base,n)=a(base-1,n)+5^(n-1)-2 when base=2n-2.
%F Conjectures from _Colin Barker_, May 31 2017: (Start)
%F G.f.: (1 + 3*x - 15*x^2 + 2*x^3 + x^4) / (1 - 7*x + 11*x^2 - x^4).
%F a(n) = 7*a(n-1) - 11*a(n-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]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))
%Y Cf. Base 10 differing by one or less A126364.
%K nonn,base
%O 0,2
%A _R. H. Hardin_, Dec 28 2006
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