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A122133
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Number of different polyominoes with maximum area of the convex hull.
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1
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1, 1, 1, 3, 5, 11, 9, 26, 22, 53, 36, 93, 64, 151, 94, 228, 143, 329, 195, 455, 271, 611, 351, 798, 460, 1021, 574, 1281, 722, 1583, 876, 1928, 1069, 2321, 1269, 2763, 1513, 3259, 1765, 3810, 2066, 4421, 2376, 5093, 2740, 5831, 3114, 6636, 3547, 7513, 3991
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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REFERENCES
| K. Bezdek, P. Brass and H. Harborth, Maximum convex hulls of connected systems of segments and of polyominoes, Beitraege Algebra Geom., Vol. 35(1) (1994), pp. 37-43
S. Kurz, Polyominoes with maximum convex hull, Diploma thesis, Bayreuth (2004)
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FORMULA
| (n^3-2n^2+4n)/16 if n mod 4 = 0, (n^3-2n^2+13n+20)/32 if n mod 4 = 1, (n^3-2n^2+4n+8)/16 if n mod 4 = 2, (n^3-2n^2+5n+8)/32 if n mod 4 =3. G.f.: (1+x-x^2-x^3+2x^5+8x^6+2x^7+4x^8+2x^9-x^10+x^12)/[(1-x^2)^2(1-x^4)^2]
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CROSSREFS
| Sequence in context: A129738 A105603 A170835 * A065019 A071328 A006538
Adjacent sequences: A122130 A122131 A122132 * A122134 A122135 A122136
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KEYWORD
| nonn
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AUTHOR
| Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 21 2006
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