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.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
Craig Knecht, H2 Hexagon with 3 heptiamonds packed in.
Craig Knecht, H3 hexagon with 7 heptiamonds packed in.
Craig Knecht, H4 H5 H6 H7 heptiamond packing.
Craig Knecht, Peripheral Buildouts.
Craig Knecht, Proof notes.
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
KEYWORD
nonn
AUTHOR
Craig Knecht, Jan 15 2018
STATUS
approved