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).

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.

Links

Paul Tek, Table of n, a(n) for n = 1..10000

Paul Tek, PERL program for this sequence

Paul Tek, Illustration of the first 1022 bricks

Paul Tek, Illustration of the first 9986 bricks

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

Adjacent sequences: A233377 A233378 A233379 * A233381 A233382 A233383

Keyword

nonn

Author

Paul Tek, Dec 08 2013

Status

approved