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

1,2

Comments

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

Links

Table of n, a(n) for n=1..22.

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Acute Triangle.

Formula

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

Example

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

Crossrefs

Cf. A190019, A241223.

Sequence in context: A264124 A317631 A309904 * A259065 A204247 A063856

Adjacent sequences: A241221 A241222 A241223 * A241225 A241226 A241227

Keyword

nonn

Author

Martin Renner, Apr 17 2014

Extensions

a(7) from Martin Renner, May 31 2014

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

Status

approved