[seqfan] Re: a question about arrangements of pennies

[Andrew Weimholt]

So far nobody has mentioned the idea of counting convex arrangements of pennies.

This appears to be in the OEIS as A116513, which is described as...

"Number of distinct hexagons of n points chosen from triangular
lattice A_2 with sides parallel to the principal axes of that lattice.
Degenerate sides (of length 1) are permitted."

It appears to me that the author intended these to be *convex* hexagons, with
degenerate sides of length *0* permitted. (A side of length 1 can
hardly be called degenerate).

A slightly simpler definition would be something like...
"Number of convex regions bound by edges of A_2 containing n vertices
of A_2 (in the interior or on the perimeter). Degenerate regions (with
area 0) are permitted."

The degenerate regions would be line segments of n vertices
(corresponding to n pennies in a row in the alternate definition).

Subtracting 1 from this sequence (i.e. removing the degenerate regions)
gives the Number of Convex Triangular Polyominoes containing n vertices of A_2.
(counting both vertices on the perimeter and in the interior of the polyominoe).
[not in OEIS].

Andrew