STATUS
reviewed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
reviewed
approved
proposed
reviewed
editing
proposed
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 binomial(n,m-1) = binomial(n-1,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
reviewed
editing
proposed
reviewed
editing
proposed
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 binomial(n,m-1) = binomial{(n-1,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
approved
editing
proposed
approved
editing
proposed
Hans Montanus and Ron Westdijk, <a href="https://matharoundtheblockgreenbluemath.eunl/wp-content/uploads/2024/03/?page_id=125Cellular-Automation-and-Binomials.pdf">Cellular Automation and Binomials</a>, Math around the Block Green Blue Mathematics (2022), p. 69.
approved
editing