%I #15 Jun 29 2020 20:42:01

%S 1,0,1,0,0,2,0,0,1,4,0,0,0,6,8,0,0,0,6,20,16,0,0,0,4,40,56,32,0,0,0,1,

%T 68,152,144,64,0,0,0,0,94,376,480,352,128,0,0,0,0,114,844,1440,1376,

%U 832,256,0,0,0,0,116,1744,4056,4736,3712,1920,512,0,0,0,0,94,3340,10856,15248,14272,9600,4352,1024

%N Upper triangular region of the table A073345.

%H Alois P. Heinz, <a href="/A073429/b073429.txt">Rows n = 0..200, flattened</a>

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000050">The depth of the binary tree.</a>

%e Triangle T(n,k) begins:

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

%e 2, 1, 0, 0, 0, 0, 0, 0, 0, ...

%e 4, 6, 6, 4, 1, 0, 0, 0, ...

%e 8, 20, 40, 68, 94, 114, 116, ...

%e 16, 56, 152, 376, 844, 1744, ...

%e 32, 144, 480, 1440, 4056, ...

%e 64, 352, 1376, 4736, ...

%e 128, 832, 3712, ...

%e 256, 1920, ...

%e 512, ...

%e ...

%p A073429 := n -> A073345bi(A003056(n), A002262(n));

%p A002262 := n -> n - binomial(floor((1/2)+sqrt(2*(1+n))),2);

%p A003056 := n -> floor(sqrt(2*(1+n))-(1/2));

%K nonn,tabl

%O 0,6

%A _Antti Karttunen_, Jul 31 2002