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Number of base 9 n-digit numbers with adjacent digits differing by two or less.
3

%I #9 Jun 01 2017 12:05:54

%S 1,9,39,175,793,3611,16475,75229,343633,1569883,7172423,32769925,

%T 149723361,684077955,3125520983,14280373781,65246447425,298108406323,

%U 1362045450407,6223131628517,28433241805745,129910355608771

%N Number of base 9 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_, Jun 01 2017: (Start)

%F G.f.: (1 + 3*x - 10*x^2 - 6*x^3 + 6*x^4 + 2*x^5) / (1 - 6*x + 5*x^2 + 8*x^3 - 4*x^4 - 2*x^5).

%F a(n) = 6*a(n-1) - 5*a(n-2) - 8*a(n-3) + 4*a(n-4) + 2*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]`-$[i+1]`>2)+($[i+1]`-$[i]`>2))

%Y Cf. Base 9 differing by one or less A126363.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 28 2006