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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.

%I A345067 #12 Jun 10 2021 15:45:38
%S A345067 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,
%T A345067 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,
%U A345067 2,4,9,4,2,15,15,15,40,15,15,6,4,4,4,4,6,15,15,40
%N 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.
%C A345067 The "Quilt Tiling" is described in Shectman's paper (see Links section).
%C A345067 All terms belong to A006498.
%H A345067 Rémy Sigrist, <a href="/A345067/b345067.txt">Table of n, a(n) for n = 1..10153</a>
%H A345067 J. Parker Shectman, <a href="http://www.ootlinc.com/Fibonacci_Quilt_2_of_3_Cohorts_and_Numeration.pdf">A Quilt after Fibonacci, Part 2 of 3: Cohorts, Free Monoids, and Numeration</a>
%H A345067 Rémy Sigrist, <a href="/A345067/a345067.png">Illustration of the connection between the "Quilt Tiling" and the sequences A000201 and A005206</a>
%H A345067 Rémy Sigrist, <a href="/A345067/a345067.gp.txt">PARI program for A345067</a>
%F A345067 T(n, k) = T(k, n).
%F A345067 T(n, n) = A130312(n+1)^2.
%F A345067 T(n, 1) = A001654(A095791(n)+1).
%F A345067 T(n, k) is the square of a Fibonacci number for n = 1+A005206(k+1)..A000201(k).
%e A345067 Array T(n, k) begins:
%e A345067   n\k|  1   2   3   4   5   6   7   8   9  10  11
%e A345067   ---+---+-------+-----------+-------------------+
%e A345067    1 |  1|  2   2|  6   6   6| 15  15  15  15  15|
%e A345067      +-----------+           |                   |
%e A345067    2 |  2|  4   4|  6   6   6| 15  15  15  15  15|
%e A345067      |   |       +---+-------+                   |
%e A345067    3 |  2|  4   4|  1|  2   2| 15  15  15  15  15|
%e A345067      +---+---+---+---+-------+-------+-----------+
%e A345067    4 |  6   6|  1|  9   9   9|  2   2|  6   6   6|
%e A345067      |       +---+           +-------+           |
%e A345067    5 |  6   6|  2|  9   9   9|  4   4|  6   6   6|
%e A345067      |       |   |           |       +---+-------+
%e A345067    6 |  6   6|  2|  9   9   9|  4   4|  1|  2   2|
%e A345067      +-------+---+---+-------+-------+---+-------+
%e A345067    7 | 15  15  15|  2|  4   4| 25  25  25  25  25|
%e A345067      |           |   |       |                   |
%e A345067    8 | 15  15  15|  2|  4   4| 25  25  25  25  25|
%e A345067      |           +---+---+---+                   |
%e A345067    9 | 15  15  15|  6   6|  1| 25  25  25  25  25|
%e A345067      |           |       +---+                   |
%e A345067   10 | 15  15  15|  6   6|  2| 25  25  25  25  25|
%e A345067      |           |       |   |                   |
%e A345067   11 | 15  15  15|  6   6|  2| 25  25  25  25  25|
%e A345067      +-----------+-------+---+-------------------+
%o A345067 (PARI) See Links section.
%Y A345067 Cf. A000045, A001654, A005206, A006498, A095791, A005206.
%K A345067 nonn,look,tabl
%O A345067 1,2
%A A345067 _Rémy Sigrist_, Jun 06 2021