User:Charles Kusniec/C000884

C000884 The original Athanasii Kircheri triangle.

In OEIS this triangle is the sequence https://oeis.org/A071797.

The sum of its y-th row is equal to $2y^{2}\pm y$, which yields the n-th hexagonal number, https://oeis.org/A000384 The square numbers plus oblong numbers.

The partial sum of the square numbers plus oblong numbers is https://oeis.org/A002412 the hexagonal pyramidal numbers, or greengrocer's numbers.

The partial differences of the square numbers plus oblong numbers is $\pm 4y+1$ https://oeis.org/A016813.

The partial differences of $\pm 4y+1$ is https://oeis.org/A010709 constant sequence: the all 4's sequence.

Source: Kircheri, P. Athanasii. (1664) Mundus Subterraneus, pg. 24, https://archive.org/details/athanasiikircher00kirc_4/page/n53/mode/2up?ref=ol&view=theater