Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence/Historical Note
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Historical Note on Rows in Pascal's Triangle containing Numbers in Arithmetic Sequence
This result, along with Rows in Pascal's Triangle containing Numbers in Geometric Sequence and Rows in Pascal's Triangle containing Numbers in Harmonic Sequence, was apparently published by Theodore Samuel Motzkin in Volume $12$ of Scripta Mathematica, but details have not been established.