login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of stones-and-bones tilings of an n-triangle.
0

%I #11 Oct 25 2024 09:37:33

%S 1,0,1,3,0,30,246,0,25321,591103,0,603105309,41333676318,0,

%T 410382321560202,83918368144461643,0,8025244898075570226296,

%U 4941312847984149589980261

%N Number of stones-and-bones tilings of an n-triangle.

%C These numbers were computed using the TilingCount program of David Desjardins. Stones are also called T_2 tiles and bones are also called L_3 tiles.

%H James Propp, <a href="http://faculty.uml.edu/jpropp/benzels.html">The Benzel Tilings Site</a>

%F a(n)=0 when n is congruent to 1 mod 3, since in that case the number of cells in the n-triangle is not divisible by 3.

%e For n=3 the three tilings are

%e A

%e A A

%e B B B

%e and

%e A

%e A B

%e A B B

%e and

%e A

%e B A

%e B B A

%Y Cf. A334875.

%K nonn,more

%O 0,4

%A _James Propp_, Oct 23 2024