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User:Joshua Giambalvo

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I am a casual mathematics enthusiast. (Can one be casually enthusiastic?) I am creating this account to share a pattern regarding n-gonal numbers that I have found, which does not yet appear to be on this website.

0, 5, 28, 81, 176, 325, 540, 833, 1216, 1701, 2300, 3025, 3888, 4901, 6706, 7425, 8960, 10693, 12636, 14801, 17200, 19845, 22748, 25921, 29376, 33125, 37180...

This sequence represents the 0th square number, the 2nd pentagonal number, the 4th hexagonal number, the 6th heptagonal number, the 8th octagonal number, the 10th nonagonal number, etc...


the 3rd "pointal" number, the 5th "linear" number, the 7th triangle number, the 9th square number, the 11th pentagonal number, the 13 hexagonal number, the 15th heptagonal number, etc...

This is a reliable pattern I have not seen anywhere else in the table of n-gonal numbers, though I would like to think that someone with more mathematical intuition than myself may be able to extract something from this, or at least be able to explain why this works.