

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.


8



0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10
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OFFSET

0,9


LINKS



FORMULA

Conjecture (derived from Euler's F+V=E+1 formula): a(n) = 1+(A069813(n)n)/2 = A001399(n6), which means g.f. is x^6 / ( (1+x)*(1+x+x^2)*(1x)^3 ).  R. J. Mathar, Jul 14 2015


EXAMPLE

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.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



