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Number of equilateral triangles, distinct up to congruence, on a centered hexagonal grid of size n.
0

%I #34 Feb 16 2025 08:33:21

%S 0,2,6,11,18,25,35,45,56,69,83,97,115,131,150,169,189,212,234,258,284

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

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HexNumber.html">Hex Number</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EquilateralTriangle.html">Equilateral Triangle</a>.

%e For n = 2 the two kinds of non-congruent equilateral triangles are the following:

%e /. * * .

%e . * * . . *

%e \. . * .

%Y Cf. A008893.

%K nonn,more,changed

%O 1,2

%A _Martin Renner_, Apr 17 2014

%E a(7) from _Martin Renner_, May 31 2014

%E a(8)-a(21) from _Giovanni Resta_, May 31 2014