A241237 Number of isosceles triangles, distinct up to congruence, on a centered hexagonal grid of size n.

0, 3, 15, 35, 69, 106, 162, 222, 300, 382, 486, 587, 715, 840, 997, 1147, 1313, 1491, 1700, 1890, 2129, 2341, 2598, 2842, 3126, 3394, 3711, 3995, 4341, 4641, 5024, 5349, 5750, 6128, 6540, 6959, 7381, 7772, 8255, 8722, 9252, 9688, 10220, 10698, 11277, 11806, 12381, 12905

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..48.

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Isosceles Triangle.

Formula

a(n) = A241231(n) - A241236(n).

Example

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

Crossrefs

Cf. A189978, A241228.

Sequence in context: A236693 A317183 A000466 * A338351 A145949 A015809

Adjacent sequences: A241234 A241235 A241236 * A241238 A241239 A241240

Keyword

nonn

Author

Martin Renner, Apr 17 2014

Extensions

a(7) from Martin Renner, May 31 2014

a(8)-a(21) from Giovanni Resta, May 31 2014

More terms from Bert Dobbelaere, Oct 17 2022

Status

approved