login
A298267
a(n) is the maximum number of heptiamonds in a hexagon of order n.
1
0, 3, 7, 13, 21, 30, 42, 54, 69, 85, 103, 123, 144, 168, 192, 219, 247, 277, 309, 342, 378, 414, 453, 493, 535, 579, 624, 672, 720, 771, 823, 877, 933, 990, 1050, 1110, 1173, 1237, 1303, 1371, 1440, 1512, 1584, 1659, 1735, 1813, 1893, 1974, 2058, 2142
OFFSET
0,2
COMMENTS
There are 24 heptiamonds.
It would be nice if this idea could be generalized to state that the hexagon can contain the maximum number of polyiamonds of any given size.
FORMULA
a(n) = floor((6*n^2)/7).
Conjectures from Colin Barker, Jan 20 2018: (Start)
G.f.: x*(1 + x)*(3 - 2*x + 4*x^2 - 2*x^3 + 3*x^4) / ((1 - x)^3*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).
a(n) = 2*a(n-1) - a(n-2) + a(n-7) - 2*a(n-8) + a(n-9) for n>8.
(End)
MATHEMATICA
Array[Floor[(6 #^2)/7] &, 50] (* Michael De Vlieger, Jan 20 2018 *)
CROSSREFS
Cf. A033581 (The number of triangles in a hexagon), A291582 (hexiamond tiling).
Sequence in context: A077853 A256588 A025721 * A235532 A195020 A169627
KEYWORD
nonn
AUTHOR
Craig Knecht, Jan 15 2018
STATUS
approved