A337131 Row lengths of irregular triangle A335967.

1, 1, 1, 1, 2, 1, 1, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 4, 8, 2, 2, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 4, 4, 16, 8, 2, 4, 2, 2, 1, 1, 2, 1, 4, 8, 2, 2, 1, 1, 4, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 4, 1, 1, 2, 2, 8, 4, 1, 2, 1, 1, 4, 4, 8, 4, 16, 32, 8

Offset: 1

Author

Rémy Sigrist, Sep 14 2020

Keywords

• nonn

Comments

All terms are powers of 2.

Examples

			For n = 13, the binary representation of 13 is "1101", so we consider the tilings of a size 4 staircase polyomino whose base has the following shape:
      .....
      .   .
      .   .....
      .       .
      +---+   .....
      |   |       .
      |   +---+---+---+
      | 1   1 | 0 | 1 |
      +-------+---+---+
There are two possible penultimate rows:
      .....              .....
      .   .              .   .
      .   .....          .   .....
      .   |   .          .       .
      +---+   +---+      +---+---+---+
      | 1 | 0   0 |      | 1 | 0 | 1 |
      |   +---+---+---+  |   +---+---+---+
      |       |   |   |  |       |   |   |
      +-------+---+---+, +-------+---+---+
so a(13) = 2.
		

Links

• Rémy Sigrist, PARI program for A337131

Crossrefs

Cf. A000975, A335967.

Programs

PARI

\\ See Links section.

Formula

a(2^k-1) = 1 for any k >= 0.

a(2^k) = 1 for any k >= 0.

a(A000975(k)) = 2^(k-2) for any k >= 2.