A257594 Consider the hexagonal lattice packing of circles; a(n) is the maximal number of circles that can be enclosed by a closed chain of n circles.
0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10
Offset: 0
Examples
In the hexagonal lattice packing of pennies, one penny can be enclosed by 6 pennies, 2 pennies by eight pennies, 3 pennies by 9 pennies, 4 pennies by 10 pennies, 5 pennies by 11 pennies, and 7 pennies by 12 pennies.
Links
- R. L. Graham and N. J. A. Sloane, Penny-Packing and Two-Dimensional Codes, Discrete and Comput. Geom. 5 (1990), 1-11.
- Craig Knecht, Classification of spaces between the pennies
- Craig Knecht, Trying to relate Sloane's 1990 findings to intercircle volumes
- R. J. Mathar, Illustration of conjectured a(9) to a(24)
- Kival Ngaokrajang, Illustration of initial terms
Crossrefs
Cf. A257481.
Formula
Conjecture (derived from Euler's F+V=E+1 formula): a(n) = 1+(A069813(n)-n)/2 = A001399(n-6), which means g.f. is x^6 / ( (1+x)*(1+x+x^2)*(1-x)^3 ). - R. J. Mathar, Jul 14 2015
Extensions
a(13) and a(14) from R. J. Mathar, Jul 10 2015