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A241231
Number of triangles, distinct up to congruence, on a centered hexagonal grid of size n.
5
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
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
Sequence in context: A053902 A054464 A002101 * A297715 A129557 A231518
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