A377309 Number of stones-and-bones tilings of an n-triangle.

1, 0, 1, 3, 0, 30, 246, 0, 25321, 591103, 0, 603105309, 41333676318, 0, 410382321560202, 83918368144461643, 0, 8025244898075570226296, 4941312847984149589980261

Offset: 0

Author

James Propp, Oct 23 2024

Keywords

• nonn
• more

Comments

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.

Examples

			For n=3 the three tilings are
      A
     A A
    B B B
and
      A
     A B
    A B B
and
      A
     B A
    B B A
		

Links

• James Propp, The Benzel Tilings Site

Crossrefs

Cf. A334875.

Formula

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.