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Number of base 10 n-digit numbers with adjacent digits differing by four or less.
1

%I #16 May 31 2017 16:55:13

%S 1,10,70,510,3720,27142,198034,1444904,10542368,76919662,561224422,

%T 4094828862,29876859864,217988781808,1590498774316,11604663002012,

%U 84670422615182,617775842744470,4507441679052256,32887382581680414

%N Number of base 10 n-digit numbers with adjacent digits differing by four or less.

%C [Empirical] a(base,n)=a(base-1,n)+9^(n-1) for base>=4n-3; a(base,n)=a(base-1,n)+9^(n-1)-2 when base=4n-4.

%F Conjectures from _Colin Barker_, May 31 2017: (Start)

%F G.f.: (1 + 3*x - 3*x^2 - 4*x^3 + x^4 + x^5) / (1 - 7*x - 3*x^2 + 6*x^3 + x^4 - x^5).

%F a(n) = 7*a(n-1) + 3*a(n-2) - 6*a(n-3) - a(n-4) + a(n-5) for n>5.

%F (End)

%o (S/R) stvar $[N]:(0..M-1) init $[]:=0 asgn $[]->{*} kill +[i in 0..N-2](($[i]`-$[i+1]`>4)+($[i+1]`-$[i]`>4))

%Y Base 10 differing by three or less A126478, two or less A126397, one or less A126364.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006