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A027709
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Minimal perimeter of polyomino with n square cells.
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6
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0, 4, 6, 8, 8, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 16, 16, 18, 18, 18, 18, 20, 20, 20, 20, 20, 22, 22, 22, 22, 22, 24, 24, 24, 24, 24, 24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 30, 30, 30, 30, 32, 32, 32, 32, 32, 32, 32, 32, 34, 34, 34, 34, 34, 34
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| a(n) = 2*A027434(n). - Tanya Khovanova (tanyakh(AT)yahoo.com), Mar 04 2008
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REFERENCES
| F. Harary and H. Harborth, Extremal Animals, Journal of Combinatorics, Information & System Sciences, Vol. 1, No 1, 1-8 (1976).
J. Yackel, R. R. Meyer and I. Christou, Minimum-perimeter domain assignment, Mathematical Programming, vol. 78 (1997), pp. 283-303
W. C. Yang, Title?, PhD Dissertation, Computer Sciences Department, University of Wisconsin-Madison, 2003.
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FORMULA
| a(n) = 2*ceil(2*sqrt(n))
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EXAMPLE
| a(5) = 10 because we can arrange 5 squares into 2 rows, with 2 squares in the top row and 3 squares in the bottom row. This shape has perimeter 10, which is minimal for 5 squares.
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MAPLE
| interface(quiet=true); for n from 0 to 100 do printf("%d, ", 2*ceil(2*sqrt(n))) od;
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CROSSREFS
| Cf. A000105, A067628 (analogue for triangles), A075777 (analogue for cubes).
Cf. A135711.
Sequence in context: A163639 A196355 A095253 * A196358 A079775 A104173
Adjacent sequences: A027706 A027707 A027708 * A027710 A027711 A027712
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Custance (jevc(AT)atml.co.uk)
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EXTENSIONS
| Edited by Winston C. Yang (winston(AT)cs.wisc.edu), Feb 02 2002
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