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A084085 Length of lists created by n substitutions k -> Range[0,Mod[k+1,4]] starting with {0}. 0

%I

%S 1,2,5,14,38,102,273,731,1958,5245,14050,37636,100816,270057,723405,

%T 1937794,5190793,13904642,37246538,99772766,267262553,715919535,

%U 1917742590,5137081001,13760762966,36861127432,98740361920,264497039329

%N Length of lists created by n substitutions k -> Range[0,Mod[k+1,4]] starting with {0}.

%C equivalent to replacements 0->{0,1}; 1->{0,1,2}; 2->{0,1,2,3}; 3->{0} operating n times with {0}.

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

%e {0}, {0,1}, {0,1,0,1,2}, {0,1,0,1,2,0,1,0,1,2,0,1,2,3} have lengths 1, 2, 5, 14.

%t Length/@Flatten/@NestList[ # /. k_Integer:>Range[0, Mod[k+1, 4]]&, {0}, 8]

%K nonn

%O 0,2

%A _Wouter Meeussen_, May 11 2003

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Last modified October 20 10:31 EDT 2019. Contains 328257 sequences. (Running on oeis4.)