Search: id:A003015
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%I A003015 M5374
%S A003015 1,120,210,1540,3003,7140,11628,24310,61218182743304701891431482520
%N A003015 Numbers that occur 5 or more times in Pascal's triangle.
%C A003015 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. - Chris Thompson (cet1(AT)cam.ac.uk), 
               Mar 09 2001
%C A003015 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 (njas(AT)research.att.com), 
               Nov 24 2004
%D A003015 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003015 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 93, #47.
%D A003015 R. K. Guy and V. Klee, Monthly research problems, 1969-1971, Amer. Math. 
               Monthly, 78 (1971), 1113-1122.
%D A003015 David Singmaster, Repeated binomial coefficients and Fibonacci numbers, 
               Fibonacci Quarterly 13 (1975) 295-298.
%H A003015 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PascalsTriangle.html">Pascal's Triangle</a>
%H A003015 B. M. M. de Weger, <a href="http://www.eur.nl/WebDOC/doc/econometrie/
               eeb19960111120006.ps">Equal binomial coefficients: some elementary 
               considerations (Postscript)</a>
%Y A003015 Cf. A003016, A059233.
%Y A003015 Sequence in context: A069790 A064224 A069674 this_sequence A098565 A084142 
               A146950
%Y A003015 Adjacent sequences: A003012 A003013 A003014 this_sequence A003016 A003017 
               A003018
%K A003015 nonn
%O A003015 1,2
%A A003015 N. J. A. Sloane (njas(AT)research.att.com).
%E A003015 No other terms below 33*10^16 (David W. Wilson (davidwwilson(AT)comcast.net)).
%E A003015 61218182743304701891431482520 really is the next term. Weger shows this 
               and I checked it. - T. D. Noe (noe(AT)sspectra.com), Nov 15 2004

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