OFFSET
1,2
COMMENTS
Equivalently, numbers of the form k^2, k^2+m^2, or 3*k^2, where k >= 1, m >= 1.
Theorem (Golomb; Snover et al.): A triangle can be partitioned into n pairwise congruent triangles iff n is of the form k^2, k^2+m^2, or 3*k^2.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Soifer, How Does One Cut A Triangle?, Chapter 2, CEME, Colorado Springs CO 1990.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Solomon W. Golomb, Replicating figures in the plane, The mathematical gazette 48.366 (1964): 403-412.
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 1".
S. Snover, Letter to N. J. A. Sloane, May 1991
S. L. Snover, C. Wavereis and J. K. Williams, Rep-tiling for triangles, Discrete Math. 91 (1991), no. 2, 193-200.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Mar 21 2001
Entry revised by N. J. A. Sloane, Nov 30 2016
STATUS
approved