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Search: id:A074764
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| A074764 |
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Numbers of smaller squares into which a square may be dissected. |
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+0
1
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| 1, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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All even n>2 are present by generalizing this corner+border construction, all odd n>5 are present because n+3 can be obtained from n by splitting any single square into four, 1 is trivially present and n=2, 3 & 5 are then fairly easily eliminated.
Also number of smaller similar triangles into which a triangle may be dissected. - Lekraj Beedassy (blekraj(AT)yahoo.com), Nov 25 2003
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REFERENCES
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A. Soifer, How Does One Cut A Triangle?, Chapter 2, CEME, Colorado Springs CO 1990.
Allan C. Wechsler and Michael Kleber, messages to math-fun mailing list, Sep 06, 2002.
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FORMULA
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n # 2, 3 or 5. G.f.(x) = x*(1-x+x^3-x^4+x^5)/(1-x)
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EXAMPLE
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6 is a member of the sequence because:
+---+---+---+
|...|...|...|
+---+---+---+
|.......|...|
|.......+---+
|.......|...|
+-------+---+
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CROSSREFS
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Sequence in context: A005670 A123860 A122817 this_sequence A101087 A138887 A031949
Adjacent sequences: A074761 A074762 A074763 this_sequence A074765 A074766 A074767
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Sep 06 2002
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