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a(n) = ceiling( log_2( Catalan(n) ) ).
1

%I #13 Sep 08 2022 08:46:18

%S 0,0,1,3,4,6,8,9,11,13,15,16,18,20,22,24,26,27,29,31,33,35,37,39,41,

%T 43,45,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,77,79,81,83,85,

%U 87,89,91,93,95,97,99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,128,130,132,134

%N a(n) = ceiling( log_2( Catalan(n) ) ).

%H Vincenzo Librandi, <a href="/A280762/b280762.txt">Table of n, a(n) for n = 0..10000</a>

%H Nils A. Baas, A Stacey, <a href="http://arxiv.org/abs/1602.06450">Investigations of Higher Order Links</a>, arXiv preprint arXiv:1602.06450, 2016. See Section 2.2.

%t Table[Ceiling[Log[CatalanNumber[n]]/Log[2]], {n, 0, 80}] (* _Vincenzo Librandi_, Jan 18 2017 *)

%o (Magma) [Ceiling(Log(Catalan(n))/Log(2)): n in [0..70]]; // _Vincenzo Librandi_, Jan 18 2017

%Y Cf. A000108.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Jan 17 2017