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Number of base 17 n-digit numbers with adjacent digits differing by three or less.
2

%I #8 Jul 18 2017 08:02:30

%S 1,17,107,693,4531,29785,196419,1297863,8586301,56847741,376551555,

%T 2494950507,16533981983,109582499195,726331242669,4814449605487,

%U 31913168495095,211543760702517,1402280350135071,9295487072185279

%N Number of base 17 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+7*x-46*x^2-44*x^3+118*x^4+63*x^5-89*x^6-27*x^7+18*x^8) / ((1-x)*(1-9*x+8*x^2+52*x^3+2*x^4-49*x^5-9*x^6+9*x^7)) (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 17 differing by two or less A126404, one or less A126371.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 27 2006