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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 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 A245231 A034154 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

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Last modified September 23 15:35 EDT 2023. Contains 365554 sequences. (Running on oeis4.)