A038666 Minimum area rectangle into which squares of sizes 1, 2, 3, ... n can be packed.

1, 6, 15, 35, 60, 99, 154, 210, 300, 405, 513, 667, 836, 1035, 1265, 1512, 1794, 2139, 2491, 2890, 3344, 3822, 4352, 4928, 5547, 6230, 6956, 7749, 8586, 9486, 10450, 11475

Offset

1,2

References

R. M. Kurchan (editor), Puzzle Fun, Number 18 (December 1997), pp. 9-10.

R. M. Kurchan (editor), Solutions of Puzzle Fun 18, Puzzle Fun, Number 22 (2000), pp. 8-10.

Links

Table of n, a(n) for n=1..32.

Jean-François Alcover, Mathematica script (after E. Pegg and R. Korf)

R. Ellard and D. MacHale, Packing Squares into Rectangles, The Mathematical Gazette, Vol. 96, No. 535 (March 2012), 1-18.

E. Huang and R. E. Korf, New Improvements in Optimal Rectangle Packing, IJCAI-09: Proceedings of the 21st International Joint Conference on Artificial Intelligence, AAAI Press, 2009, pages 511-516. (Table 1 incorrectly lists the 95 X 110 minimal rectangle for n = 31 as 91 X 110.)

Ed Pegg, Jr., Illustration of 17th term

Formula

a(n) = A000330(n) + A081287(n). - Pontus von Brömssen, Mar 01 2024

Crossrefs

Cf. A000330, A081287.

Sequence in context: A245630 A357848 A049728 * A075625 A006094 A379232

Adjacent sequences: A038663 A038664 A038665 * A038667 A038668 A038669

Keyword

nonn,more

Author

Erich Friedman

Extensions

Corrected and extended by William Rex Marshall, Mar 23 2002 and Aug 29 2002

a(22)-a(32) from Korf, communicated by William Rex Marshall, May 03 2012

Status

approved