
COMMENTS

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 m1} = {n1 choose m} given by n = F_{2k}F_{2k+1}; m = F_{2k1}F_{2k} where F_i is the ith Fibonacci number. The first of these outside the range of the existing database entry is {104 choose 39} = {103 choose 40}= 61218182743304701891431482520.  Chris Thompson (cet1(AT)cam.ac.uk), 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


REFERENCES

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 93, #47.
R. K. Guy and V. Klee, Monthly research problems, 19691971, Amer. Math. Monthly, 78 (1971), 11131122.
David Singmaster, Repeated binomial coefficients and Fibonacci numbers, Fibonacci Quarterly 13 (1975) 295298.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
