A241223 Number of triangles on a centered hexagonal grid of size n.

0, 32, 900, 7380, 34676, 118044, 325872, 775856, 1653888, 3237984, 5923028, 10249596, 16938588, 26924036, 41393424, 61830480, 90059672, 128293728, 179185500, 245889068, 332107188, 442162836, 581060024, 754545360, 969196896, 1232477192, 1552824900

Offset

1,2

Comments

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Triangle.

Formula

a(n) = A240826(n) - A241222(n).

a(n) = A241224(n) + A241225(n) + A241226(n) = A241227(n) + A241228(n).

Example

For n = 2 the 32 triangles are the following:
/. *     * *     * .     . .     . .     . .     . *     * *
. * *   . * .   * * .   * * .   . * .   . * *   * . *   . . .
\. .     . .     . .     * .     * *     . *     . .     * .
-
/* .     . .     . *     * .     . *     * *     * .     . *
* . .   * . *   . . .   . . *   . . *   . . .   * . *   * . .
\. *     * .     * *     . *     * .     . *     . .     * .
-
/* .     . .     * *     * *     * .     . .     . .     . *
. . .   * . *   . . *   * . .   * . .   * . .   . . *   . . *
\* *     . *     . .     . .     * .     * *     * *     . *
-
/* .     . *     * .     . .     . .     . *     * .     . *
. * *   * * .   . * .   * * .   . * *   . * .   . . *   * . .
\. .     . .     * .     . *     * .     . *     * .     . *

Crossrefs

Cf. A045996.

Sequence in context: A222606 A283854 A160314 * A283412 A227441 A067820

Adjacent sequences: A241220 A241221 A241222 * A241224 A241225 A241226

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

Terms a(23) and beyond from Andrew Howroyd, Sep 18 2017

Status

approved