|
Search: id:A074764
|
|
|
| A074764 |
|
Numbers of smaller squares into which a square may be dissected. |
|
+0
1
|
|
| 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)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
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.
|
|
FORMULA
|
n # 2, 3 or 5. G.f.(x) = x*(1-x+x^3-x^4+x^5)/(1-x)
|
|
EXAMPLE
|
6 is a member of the sequence because:
+---+---+---+
|...|...|...|
+---+---+---+
|.......|...|
|.......+---+
|.......|...|
+-------+---+
|
|
CROSSREFS
|
Adjacent sequences: A074761 A074762 A074763 this_sequence A074765 A074766 A074767
Sequence in context: A005670 A123860 A122817 this_sequence A101087 A138887 A031949
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Marc LeBrun (mlb(AT)well.com), Sep 06 2002
|
|
|
Search completed in 0.002 seconds
|
