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A233380
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).
2
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, 53, 49, 40, 25, 0, 114, 97, 81, 78, 70, 56, 32, 0, 147, 131, 116, 114, 107, 94, 71, 40, 0, 188, 173, 159, 158, 152, 140, 118, 88, 49, 0, 238, 224, 211, 298, 285
OFFSET
1,4
COMMENTS
We tile the first quadrant according to the following rules:
(a) We use bricks of height 1 and width 1, 2, 3, ...
(b) The bricks are laid by increasing size, without overlap.
(c) The left border of any brick must lie on the Y-axis or match the right border of a smaller brick.
(d) The bottom border of any brick must lie on the X-axis or touch all along the top border of smaller bricks.
(e) When multiple positions are possible, we choose the leftmost one.
A233381 gives the Y-coordinate.
EXAMPLE
The following diagram depicts the first 7 bricks:
+-------------+
| 7 |
+-----+-------+---+
| 3 | 6 |
+-+---+-------+---+-----+
|1| 2 | 4 | 5 |
+-+---+-------+---------+---> X
0 1 2 3 4 5 6 7 8 9 ...
Hence:
a(1)=a(3)=a(7)=0
a(2)=1
a(4)=a(6)=3
a(5)=7
PROG
(Perl) See Link section.
CROSSREFS
Cf. A233381.
Sequence in context: A347772 A248214 A144713 * A320027 A134731 A133368
KEYWORD
nonn
AUTHOR
Paul Tek, Dec 08 2013
STATUS
approved