A241231 Number of triangles, distinct up to congruence, on a centered hexagonal grid of size n.

0, 4, 34, 134, 379, 866, 1718, 3085, 5149, 8095, 12188, 17664, 24781, 33861, 45269, 59327, 76461, 97017, 121458, 150379, 184053, 223137, 268117, 319578, 378132, 444455, 519178, 602675, 696102, 800051, 914995, 1042094, 1181858, 1335414, 1503251, 1686811, 1886417, 2103007

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..38.

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Triangle.

Formula

a(n) = A241232(n) + A241233(n) + A241234(n) = A241236(n) + A241237(n).

Example

For n = 2 the four kinds of non-congruent triangles are the following:
/. *     * *     . *     * .
. * *   . . *   * . *   . . *
\. .     . .     . .     * .

Crossrefs

Cf. A028419, A241223.

Sequence in context: A053902 A054464 A002101 * A297715 A129557 A231518

Adjacent sequences: A241228 A241229 A241230 * A241232 A241233 A241234

Keyword

nonn

Author

Martin Renner, Apr 17 2014

Extensions

a(7) from Martin Renner, May 31 2014

a(8)-a(14) from Giovanni Resta, May 31 2014

More terms from Bert Dobbelaere, Oct 17 2022

Status

approved