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Number of base 21 n-digit numbers with adjacent digits differing by three or less.
2

%I #9 Jul 19 2017 07:34:23

%S 1,21,135,889,5903,39389,263647,1768457,11880131,79895207,537729241,

%T 3621234957,24396753479,164414536077,1108268954317,7471720473245,

%U 50378750794147,339712511249557,2290882896563443,15449485988902675

%N Number of base 21 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 G.f.: (1+9*x-84*x^2-2*x^3+321*x^4+70*x^5-178*x^6-26*x^7+13*x^8+2*x^9) / (1-12*x+33*x^2+36*x^3-125*x^4-55*x^5+70*x^6+16*x^7-5*x^8-x^9) (conjectured). - _Colin Barker_, Jul 18 2017

%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 21 differing by two or less A126408, one or less A126375.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 27 2006