A241232 Number of acute triangles, distinct up to congruence, on a centered hexagonal grid of size n.

0, 2, 14, 49, 134, 296, 580, 1034, 1720, 2691, 4043, 5841, 8193, 11178, 14935, 19567, 25197, 31954, 40006, 49521, 60596, 73442, 88238, 105158, 124432, 146220, 170802, 198278, 228999, 263185, 300988, 342775, 388775, 439269, 494462, 554839, 620474, 691717, 769060, 852639

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..40.

Eric Weisstein's World of Mathematics, Hex Number.

Eric Weisstein's World of Mathematics, Acute Triangle.

Formula

a(n) = A241231(n) - A241233(n) - A241234(n)

Example

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

Crossrefs

Cf. A190021, A241224.

Sequence in context: A270666 A330544 A056080 * A163796 A153978 A214908

Adjacent sequences: A241229 A241230 A241231 * A241233 A241234 A241235

Keyword

nonn

Author

Martin Renner, Apr 17 2014

Extensions

a(7) from Martin Renner, May 31 2014

a(8)-a(18) from Giovanni Resta, May 31 2014

More terms from Bert Dobbelaere, Oct 17 2022

Status

approved