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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,9
LINKS
R. L. Graham and N. J. A. Sloane, Penny-Packing and Two-Dimensional Codes, Discrete and Comput. Geom. 5 (1990), 1-11.
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
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
Cf. A257481.
Sequence in context: A056759 A101511 A111747 * A101545 A245231 A034154
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, May 18 2015
EXTENSIONS
a(13) and a(14) from R. J. Mathar, Jul 10 2015
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)