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

1,5

Comments

All terms are powers of 2.

Links

Table of n, a(n) for n=1..86.

Rémy Sigrist, PARI program for A337131

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.

Example

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.

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A000975, A335967.

Sequence in context: A098873 A377063 A257462 * A046876 A026584 A396348

Adjacent sequences: A337128 A337129 A337130 * A337132 A337133 A337134

Keyword

nonn

Author

Rémy Sigrist, Sep 14 2020

Status

approved