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Number of base 11 n-digit numbers with adjacent digits differing by three or less.
2

%I #11 Jul 18 2017 01:46:26

%S 1,11,65,399,2473,15381,95757,596341,3714153,23133309,144085281,

%T 897434333,5589669241,34815260805,216846906193,1350631326317,

%U 8412409590489,52396708044853,326352989158113,2032690173290461

%N Number of base 11 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+4*x-10*x^2-16*x^3+6*x^4+8*x^5) / (1-7*x+2*x^2+18*x^3-2*x^4-8*x^5) (conjectured). - _Colin Barker_, Jul 17 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 11 differing by two or less A126398, one or less A126365.

%K nonn,base

%O 0,2

%A _R. H. Hardin_, Dec 27 2006