This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003015 Numbers that occur 5 or more times in Pascal's triangle.
(Formerly M5374)
1, 120, 210, 1540, 3003, 7140, 11628, 24310, 61218182743304701891431482520 (list; graph; refs; listen; history; text; internal format)



The subject of a recent thread on sci.math. Apparently it has been known for many years that there are infinitely many numbers that occur at least 6 times in Pascal's triangle, namely the solutions to {n choose m-1} = {n-1 choose m} given by n = F_{2k}F_{2k+1}; m = F_{2k-1}F_{2k} where F_i is the i-th Fibonacci number. The first of these outside the range of the existing database entry is {104 choose 39} = {103 choose 40}= 61218182743304701891431482520. - Christopher E. Thompson, Mar 09 2001

It may be that there are no terms that appear exactly 5 times in Pascal's triangle, in which case the title could be changed to "Numbers that occur 6 or more times in Pascal's triangle". - N. J. A. Sloane, Nov 24 2004

No other terms below 33*10^16 (David W. Wilson).

61218182743304701891431482520 really is the next term. Weger shows this and I checked it. - T. D. Noe, Nov 15 2004


L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 93, #47.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..9.

B. M. M. de Weger, Equal binomial coefficients: some elementary considerations (Postscript)

R. K. Guy and V. Klee, Monthly research problems, 1969-1971, Amer. Math. Monthly, 78 (1971), 1113-1122.

David Singmaster, Repeated binomial coefficients and Fibonacci numbers, Fibonacci Quarterly 13 (1975) 295-298.

Eric Weisstein's World of Mathematics, Pascal's Triangle


Cf. A003016, A059233.

Cf. A182237, A098565 (subsequence).

Sequence in context: A069790 A064224 A069674 * A098565 A084142 A256814

Adjacent sequences:  A003012 A003013 A003014 * A003016 A003017 A003018




N. J. A. Sloane



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 07:23 EST 2015. Contains 264487 sequences.