A257594 - OEIS

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

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OFFSET

0,9

LINKS

Table of n, a(n) for n=0..14.

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

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 A375857 A245231

Adjacent sequences: A257591 A257592 A257593 * A257595 A257596 A257597

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