  The number of Young Tableaux whose shape is a k by n rectangle is famously
(nk)! 0! ... (k-1)!/((n+k-1)!(n+k-2)!... n!) implying that for each specific k,
that sequence satisfies a linear recurrence equation with polynomial
coefficients of the first order. But what about counting Young tableaux where
certain "run lengths" are forbidden? Then things seem to get much more
complicated. We conclude with four conjectures and pledge donations to the OEIS
in honor of the first provers.
