A299780 - OEIS

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.

%I #27 Jul 05 2019 18:48:13

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

%N 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.

%C Taken from _Brian Galebach_'s square array (see link).

%H Brian L. Galebach, <a href="http://ProbabilitySports.com/tilings.html">n-Uniform Tilings</a>

%H José Ezequiel Soto Sánchez, Asla Medeiros e Sá, Luiz Henrique de Figueiredo, <a href="https://doi.org/10.1007/s00371-019-01665-y">Acquiring periodic tilings of regular polygons from images</a>, The Visual Computer (2019) Vol. 35, Issue 6-8, 899-907.

%e Triangle begins:

%e 11;

%e 0, 20;

%e 0, 22, 39;

%e 0, 33, 85, 33;

%e 0, 74, 149, 94, 15;

%e 0, 100, 284, 187, 92, 10;

%e ...

%e 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.

%Y Row sums gives A068599.

%Y Leading diagonal is A068600.

%Y Column 1 gives 11 together with A000004.

%Y Cf. A299781, A299782.

%K nonn,tabl,hard,more

%O 1,1

%A _Omar E. Pol_, Mar 30 2018