A299782 -id:A299782 - cp's OEIS frontend

A299780 Triangle read by rows: T(n,m) = number of n-uniform tilings having m different arrangements of polygons about their vertices, n >= 1 and 1 <= m <= n.

11, 0, 20, 0, 22, 39, 0, 33, 85, 33, 0, 74, 149, 94, 15, 0, 100, 284, 187, 92, 10, 0

Offset: 1

Omar E. Pol, Mar 30 2018

Taken from Brian Galebach's square array (see link).

			Triangle begins:
  11;
   0,  20;
   0,  22,  39;
   0,  33,  85,  33;
   0,  74, 149,  94, 15;
   0, 100, 284, 187, 92, 10;
...
Other known positive terms are T(7,7) = 7, T(8,7) = 20, T(9,8) = 8, T(10,8) = 27 and T(11,9) = 1.

Brian L. Galebach, n-Uniform Tilings
José Ezequiel Soto Sánchez, Asla Medeiros e Sá, Luiz Henrique de Figueiredo, Acquiring periodic tilings of regular polygons from images, The Visual Computer (2019) Vol. 35, Issue 6-8, 899-907.

Row sums gives A068599.
Leading diagonal is A068600.
Column 1 gives 11 together with A000004.
Cf. A299781, A299782.

A299781 Triangle read by rows: T(n,m) = number of k-uniform tilings having m different arrangements of polygons about their vertices, for k = 1..n, with 1 <= m <= n.

Original entry on oeis.org

11, 11, 20, 11, 42, 39, 11, 75, 124, 33, 11, 149, 273, 127, 15, 11, 249, 557, 314, 107, 10, 11

Offset: 1

Omar E. Pol, Mar 30 2018

Column m lists the partial sums of the m-th column of triangle A299780.

			Triangle begins:
  11;
  11,  20;
  11,  42,  39;
  11,  75, 124,  33;
  11, 149, 273, 127,  15;
  11, 249, 557, 314, 107, 10;
...

Brian L. Galebach, n-Uniform Tilings

Column 1 gives A010850.
Leading diagonal is A068600.
Row sums give A299782.
Cf. A068599, A299780.

cp's OEIS Frontend

A299780 Triangle read by rows: T(n,m) = number of n-uniform tilings having m different arrangements of polygons about their vertices, n >= 1 and 1 <= m <= n.

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