Pascal Triangle Diagonal Sums
The paper gives an explicit formula for sums over arbitrary diagonals kx+my=n in classical Pascal's triangle. The paper proves that the diagonal-sum sequence is a shifted version of the division-count sequence. Green had shown that fixed c…
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The paper gives an explicit formula for sums over arbitrary diagonals kx+my=n in classical Pascal's triangle. The paper proves that the diagonal-sum sequence is a shifted version of the division-count sequence. Green had shown that fixed coprime k,m diagonal-sum sequences satisfy the same two-lag recurrence for n at least m. The final diagonal-sum formula computes the diagonal quantity without directly solving kx+my=n.