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

%I A377309 #11 Oct 25 2024 09:37:33
%S A377309 1,0,1,3,0,30,246,0,25321,591103,0,603105309,41333676318,0,
%T A377309 410382321560202,83918368144461643,0,8025244898075570226296,
%U A377309 4941312847984149589980261
%N A377309 Number of stones-and-bones tilings of an n-triangle.
%C A377309 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 A377309 James Propp, <a href="http://faculty.uml.edu/jpropp/benzels.html">The Benzel Tilings Site</a>
%F A377309 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 A377309 For n=3 the three tilings are
%e A377309       A
%e A377309      A A
%e A377309     B B B
%e A377309 and
%e A377309       A
%e A377309      A B
%e A377309     A B B
%e A377309 and
%e A377309       A
%e A377309      B A
%e A377309     B B A
%Y A377309 Cf. A334875.
%K A377309 nonn,more
%O A377309 0,4
%A A377309 _James Propp_, Oct 23 2024