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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.
3
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.
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
KEYWORD
nonn,base,tabf,look
AUTHOR
Rémy Sigrist, Sep 14 2020
STATUS
approved