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A345067
Consider the "Quilt Tiling"; T(n, k) is the area of the tile containing the unit square whose upper right corner has coordinates (n, k); square array T(n, k) read by antidiagonals upwards, n, k > 0.
2
1, 2, 2, 2, 4, 2, 6, 4, 4, 6, 6, 6, 4, 6, 6, 6, 6, 1, 1, 6, 6, 15, 6, 2, 9, 2, 6, 15, 15, 15, 2, 9, 9, 2, 15, 15, 15, 15, 15, 9, 9, 9, 15, 15, 15, 15, 15, 15, 2, 9, 9, 2, 15, 15, 15, 15, 15, 15, 2, 4, 9, 4, 2, 15, 15, 15, 40, 15, 15, 6, 4, 4, 4, 4, 6, 15, 15, 40
OFFSET
1,2
COMMENTS
The "Quilt Tiling" is described in Shectman's paper (see Links section).
All terms belong to A006498.
FORMULA
T(n, k) = T(k, n).
T(n, n) = A130312(n+1)^2.
T(n, 1) = A001654(A095791(n)+1).
T(n, k) is the square of a Fibonacci number for n = 1+A005206(k+1)..A000201(k).
EXAMPLE
Array T(n, k) begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11
---+---+-------+-----------+-------------------+
1 | 1| 2 2| 6 6 6| 15 15 15 15 15|
+-----------+ | |
2 | 2| 4 4| 6 6 6| 15 15 15 15 15|
| | +---+-------+ |
3 | 2| 4 4| 1| 2 2| 15 15 15 15 15|
+---+---+---+---+-------+-------+-----------+
4 | 6 6| 1| 9 9 9| 2 2| 6 6 6|
| +---+ +-------+ |
5 | 6 6| 2| 9 9 9| 4 4| 6 6 6|
| | | | +---+-------+
6 | 6 6| 2| 9 9 9| 4 4| 1| 2 2|
+-------+---+---+-------+-------+---+-------+
7 | 15 15 15| 2| 4 4| 25 25 25 25 25|
| | | | |
8 | 15 15 15| 2| 4 4| 25 25 25 25 25|
| +---+---+---+ |
9 | 15 15 15| 6 6| 1| 25 25 25 25 25|
| | +---+ |
10 | 15 15 15| 6 6| 2| 25 25 25 25 25|
| | | | |
11 | 15 15 15| 6 6| 2| 25 25 25 25 25|
+-----------+-------+---+-------------------+
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,look,tabl
AUTHOR
Rémy Sigrist, Jun 06 2021
STATUS
approved