A241224 Number of acute triangles on a centered hexagonal grid of size n.

0, 8, 204, 1788, 8690, 30360, 85194, 205394, 441876, 870912, 1601708, 2783574, 4616220, 7358312, 11339430, 16972182, 24763604, 35328426, 49405944, 67873484, 91762128, 122276784

Offset: 1

Author

Martin Renner, Apr 17 2014

Keywords

• nonn

Comments

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

Examples

			For n = 2 the eight acute triangles are the following:
/. *     * *     * .     . .     . .     . .     * .     . *
. * *   . * .   * * .   * * .   . * .   . * *   . . *   * . .
\. .     . .     . .     * .     * *     . *     * .     . *
		

Links

• Eric Weisstein's World of Mathematics, Hex Number.
• Eric Weisstein's World of Mathematics, Acute Triangle.

Crossrefs

Cf. A190019, A241223.

Formula

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

Extensions

a(7) from Martin Renner, May 31 2014

a(8)-a(22) from Giovanni Resta, May 31 2014