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A074764 Numbers of smaller squares into which a square may be dissected. 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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, Nov 25 2003

REFERENCES

Laczkovich, Miklós. "Tilings of polygons with similar triangles." Combinatorica10.3 (1990): 281-306.

Laczkovich, Miklós. "Tilings of triangles." Discrete mathematics 140.1 (1995): 79-94.

Laczkovich, Miklós. "Tilings of polygons with similar triangles, II." Discrete & Computational Geometry 19.3 (1998): 411-425.

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.

Zak, Andrzej. "Dissection of a triangle into similar triangles." Discrete & Computational Geometry 34.2 (2005): 295-312.

LINKS

Table of n, a(n) for n=1..71.

Mr. Glaeser, Carrés, Le Petit Archimède, no. 0, January 1973

Murray Klamkin, Review of "How Does One Cut a Triangle?" by Alexander Soifer, Amer. Math. Monthly, October 1991, pp. 775-. [Annotated scanned copy of pages 775-777 only] See "Grand Problem 2".

FORMULA

n # 2, 3 or 5.

G.f.: x*(1 - x + x^3 - x^4 + x^5)/(1-x).

EXAMPLE

6 is a term of the sequence because:

+---+---+---+

|...|...|...|

+---+---+---+

|.......|...|

|.......+---+

|.......|...|

+-------+---+

CROSSREFS

Cf. A005792.

Sequence in context: A234948 A123860 A122817 * A101087 A138887 A216845

Adjacent sequences:  A074761 A074762 A074763 * A074765 A074766 A074767

KEYWORD

easy,nonn

AUTHOR

Marc LeBrun, Sep 06 2002

STATUS

approved

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Last modified November 15 19:18 EST 2019. Contains 329149 sequences. (Running on oeis4.)