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Number of acute triangles on a centered hexagonal grid of size n.
4

%I #10 May 31 2014 10:39:02

%S 0,8,204,1788,8690,30360,85194,205394,441876,870912,1601708,2783574,

%T 4616220,7358312,11339430,16972182,24763604,35328426,49405944,

%U 67873484,91762128,122276784

%N Number of acute triangles on a centered hexagonal grid of size n.

%C A centered hexagonal grid of size n is a grid with A003215(n-1) points forming a hexagonal lattice.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexNumber.html">Hex Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AcuteTriangle.html">Acute Triangle</a>.

%F a(n) = A241223(n) - A241225(n) - A241226(n).

%e For n = 2 the eight acute triangles are the following:

%e /. * * * * . . . . . . . * . . *

%e . * * . * . * * . * * . . * . . * * . . * * . .

%e \. . . . . . * . * * . * * . . *

%Y Cf. A190019, A241223.

%K nonn

%O 1,2

%A _Martin Renner_, Apr 17 2014

%E a(7) from _Martin Renner_, May 31 2014

%E a(8)-a(22) from _Giovanni Resta_, May 31 2014