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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 polynomialcoefficients of the first order. But what about counting Young tableaux wherecertain "run lengths" are forbidden? Then things seem to get much morecomplicated. We conclude with four conjectures and pledge donations to the OEISin honor of the first provers.

Counting Standard Young Tableaux With Restricted Runs