زیبایی‌های مثلث خیام-پاسکال

[1] H. L. Abbott, P. Erdős and D. Hanson, On the number of times an integer occurs as a binomial coefficient, Amer. Math. Monthly, 81 (1974) 256-261.
[2] S. Ando, A triangular array with hexagon property, dual to Pascal’s triangle, Applications of Fibonacci Numbers, (San Jose, CA, 1986), Kluwer Acad. Publ., Dordrecht, 1988 61–67.
[3] A. T. Benjamin and J. J. Quinn, Proofs that really count: The art of combinatorial proof, The Dolciani Mathematical Expositions, 27, Mathematical Association of America, Washington, DC, 2003.
[4] A. Bogomolny, Patterns in Pascal’s triangle-From Cut the Knot (1996–2018), https://www.cut-the-knot.org/arithmetic/combinatorics/PascalTriangleProperties.shtml.
[5] D. Brink, Nilakantha’s accelerated series for  , Acta Arith., 171 (2015) 293–308.
[6] H. J. Brothers, Math bite: Finding e in Pascal’s triangle, Math. Mag., 85 (2012).
[7] L. O. Cannon, Locating multiples of primes in Pascal’s triangle, College Math. J., 20 (1989) 324–328.
[8] J. L. Coolidge, The story of the binomial theorem, Amer. Math. Monthly, 56 (1949) 147–157.
[9] T. Edgar, Proof without words: sums of reciprocals of binomial coefficients, Math. Mag., 89 (2016) 212–213.
[10] N. J. Fine, Binomial coefficients modulo a prime, Amer. Math. Monthly, 54 (1947) 589–592.
[11] T. Foster, Nilakantha’s footprints in Pascal’s triangle, Math. Teacher, 108 (2014) 247–248.
[12] A. Gupta, Generalized hidden hexagon squares, Fibonacci Quart., 12 (1974) 45–46.
[13] R. C. Gupta, Varahamihira’s calculation of n C r and the discovery of pascal’s triangle, Ganita Bharati, 14 (1992) 45–49.
[14] H. Harborth, Number of odd binomial coefficients, Proc. Amer. Math. Soc., 62 (1977) 19–22.
[15] P. Hilton, D. Holton and J. Pedersen, Mathematical Reflections: In a Room with Many Mirrors, Springer-Verlag, New York, 1997.
[16] P. Hilton and J. Pedersen, Looking into Pascal’s triangle, Math. Mag., 60 (1987) 305–316.
[17] V. E. Hoggatt and W. Hansell, The hidden hexagon squares, Fibonacci Quart., 9 (1971) 120–133.
[18] D. M. Kane, Improved bounds on the number of ways of expressing t as a binomial coefficient, Integers, 7 (2007) 1–7.
[19] V. J. Katz and K. H. Parshall, Taming the Unknown: A History of Algebra from Antiquity to the Early Twentieth Century, Princeton University Press, Princeton, 2014.
[20] T. Koshy, Fibonacci and Lucas Numbers with Applications, 1, John Wiley & Sons, Inc., New York, 2018.
[21] V. H. Moll, Numbers and Functions: From a Classical-Experimental Mathematician’s Point of View, AMS, Provi-dence, Rhode Island, 2012.
[22] G. Pólya, R. E. Tarjan and D. R. Woods, Notes on Introductory Combinatorics, Springer Science & Business Media, New York, 1983.
[23] R. Rashed, The Development of Arabic Mathematics: Between Arithmetic and Algebra, translated from the 1984 French original by A. F. W. Armstrong, Kluwer Academic Publishers, Dordrecht, 1994.
[24] A. M. Rockett, Sums of the inverses of binomial coefficients, Fibonacci Quart., 19 (1981) 433–437.
[25] R. Roy, Sources in the Development of Mathematics: Series and Products from the Fifteenth to the Twenty-First Century, Cambridge University Press , Cambridge, 2011.
[26] R. Roy, The discovery of the series formula for  by Leibniz, Gregory and Nilakantha, Math. Mag., 63 (1990) 291–306.
[27] D. Singmaster, How often does an integer occur as a binomial coefficient?, Amer. Math. Monthly, 78 (1971) 385–386.
[28] K. J. Smith, Pascal’s triangle, Two-Year College Math. J., 4 (1973) 1–13.
[29] M. Z. Spivey, The Art of Proving Binomial Identities, CRC Press, New York, 2019.
[30] Z. Usiskin, Perfect square patterns in the Pascal triangle, Math. Mag., 46 (1973) 203–208.
[31] J. Varnadore, Pascal’s triangle and Fibonacci numbers, Math. Teacher, 84 (1991) 314–319.
[32] S. Wolfram, Geometry of binomial coefficients, Amer. Math. Monthly, 91 (1984) 566–571.

[33] ج. بهبودیان، م. بیات، و ح. تیموری فعال، مثلث عددی خیام-پاسکال و مثلثهای شبیه آن،  انتشارات علمی دانشگاه صنعتی شریف، تهران، 1385.

[34] ب. کوچک شوشتری, اعداد کاتالان, فرهنگ و اندیشه ریاضی, 46 (1390) 57--72.

[35] ح. محمودیان، شگفتی‌های مثلث خیام: گذری بر آنالیز ترکیبی، امید کورش، تهران، 1386.

[36] م. میرزاوزیری، شمردنی‌ها را بشمار، آهنگ قلم، مشهد، 1390.