A335967 Irregular table read by rows; if the binary representation of n encodes the last row of a tiling of a staircase polyomino, then the n-th row contains the numbers k whose binary representation encode possible penultimate rows.

0, 1, 1, 2, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 5, 6, 5, 4, 5, 6, 7, 8, 9, 10, 11, 10, 9, 10, 13, 14, 8, 9, 10, 11, 12, 13, 14, 15, 10, 13, 11, 12, 11, 10, 8, 9, 10, 11, 9, 10, 13, 12, 13, 14, 15, 16, 17, 18, 19, 18, 21, 22, 20, 21, 22, 23, 21, 20, 19, 20, 27, 28

Offset

1,4

Comments

We consider tilings of staircase polyominoes as described in A335547, and encode rows of such tilings as described in A336479.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..6766 (rows 1..2^10)

Rémy Sigrist, Scatterplot of the terms of the first 2^16 rows, flattened

Rémy Sigrist, PARI program for A335967

Index entries for sequences related to binary expansion of n

Formula

A336479(n) = Sum_{k = 1..A337131(n)} A336479(T(n, k)).

Example

Triangle begins:
     1: [0]
     2: [1]
     3: [1]
     4: [2]
     5: [2, 3]
     6: [2]
     7: [3]
     8: [4]
     9: [5]
    10: [4, 5, 6, 7]
    11: [5, 6]
    12: [5]
    13: [4, 5]
    ...
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 the 13th row contains 4 and 5 ("100" and "101" in binary).

Prog

(PARI) See Links section.

Crossrefs

Cf. A101211, A335547, A336479, A337131 (row lengths).

Sequence in context: A318287 A048621 A308048 * A319611 A337102 A239495

Adjacent sequences: A335964 A335965 A335966 * A335968 A335969 A335970

Keyword

nonn,base,tabf,look

Author

Rémy Sigrist, Sep 14 2020

Status

approved