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%I #14 Apr 25 2016 12:00:16
%S 0,1,0,3,7,3,0,12,9,7,0,20,18,17,11,0,32,31,49,68,49,31,26,16,0,88,70,
%T 53,49,40,25,0,114,97,81,78,70,56,32,0,147,131,116,114,107,94,71,40,0,
%U 188,173,159,158,152,140,118,88,49,0,238,224,211,298,285
%N X-coordinate of the bottom left corner of the n X 1 brick in the greedy tiling of the first quadrant with bricks of height 1 and width 1, 2, 3... (See Comments for precise definition).
%C We tile the first quadrant according to the following rules:
%C (a) We use bricks of height 1 and width 1, 2, 3, ...
%C (b) The bricks are laid by increasing size, without overlap.
%C (c) The left border of any brick must lie on the Y-axis or match the right border of a smaller brick.
%C (d) The bottom border of any brick must lie on the X-axis or touch all along the top border of smaller bricks.
%C (e) When multiple positions are possible, we choose the leftmost one.
%C A233381 gives the Y-coordinate.
%H Paul Tek, <a href="/A233380/b233380.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Tek, <a href="/A233380/a233380.txt">PERL program for this sequence</a>
%H Paul Tek, <a href="/A233380/a233380.png">Illustration of the first 1022 bricks</a>
%H Paul Tek, <a href="/A233380/a233380_1.png">Illustration of the first 9986 bricks</a>
%e The following diagram depicts the first 7 bricks:
%e +-------------+
%e | 7 |
%e +-----+-------+---+
%e | 3 | 6 |
%e +-+---+-------+---+-----+
%e |1| 2 | 4 | 5 |
%e +-+---+-------+---------+---> X
%e 0 1 2 3 4 5 6 7 8 9 ...
%e Hence:
%e a(1)=a(3)=a(7)=0
%e a(2)=1
%e a(4)=a(6)=3
%e a(5)=7
%o (Perl) See Link section.
%Y Cf. A233381.
%K nonn
%O 1,4
%A _Paul Tek_, Dec 08 2013
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