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A337131 Row lengths of irregular triangle A335967. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A098120 A098873 A257462 * A046876 A026584 A247342

Adjacent sequences:  A337128 A337129 A337130 * A337132 A337133 A337134

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Sep 14 2020

STATUS

approved

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Last modified October 26 04:45 EDT 2021. Contains 348256 sequences. (Running on oeis4.)