[seqfan] Do the numbers of A032123 always occur exactly five times in Losanitsch's triangle?

Alonso Del Arte alonso.delarte at gmail.com
Thu Mar 12 16:47:23 CET 2009

In the course of calculating the Losanitsch counterpart for A003016, I
looked up 4, 10, 38, 126, 472, numbers < 500 that occur five times in
Losanitsch's triangle. The result was A032123, which is the number of
2n-bead black-white reversible strings with n black beads, and also
the central column of Losanitsch's triangle.

With the obvious exception of 1 (which occurs infinitely often), it
seems that these numbers occur exactly five times in Losanitsch's
triangle: once in the central column, twice in column 1 a bit further
down, and twice again in column n - 1 symmetrically to column 1. The
hard part might be to prove that they don't occur anywhere else.

Alonso del Arte

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