[vgklplcp] Magic hexagon

Place numbers in a grid in the shape of a hexagon.  The standard constraint is that every complete row have the same sum, even though some rows have more numbers than others (in contrast to a magic square).  There exists such a unique magic hexagon of order 3.

A "weaker" constraint is to require any three (etc) adjacent numbers in a line to have the same sum.  For rows with greater than 3 numbers, the sums are over partial rows.  For more magic, one might also require every triangular cluster of three numbers also have that sum.  I imagine 3-element sum templates being overlaid on a pattern of numbers.

Another weaker constraint would be to require rows sum to R*X, where R is the number of elements in the full row, and X is the "pre-scaled" magic constant.