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四面體數 - Wikipedia

四面體數

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五層高的錐體
五層高的錐體

四面體數三角錐體數是可以排成底為三角形的錐體(即四面體)的數。四面體數每層為三角形數,其公式是首n個三角形數之和,即n(n + 1)(n + 2) / 6。其首幾項為:1, 4, 10, 20, 35, 56, 84, 120...(OEIS:A000292

四面體數的奇偶排列是「奇偶偶偶」。

1878年,A.J. Meyl證明只有3個四面體數同時為平方數:1, 4, 19600。唯一同時是四面體數和正方錐數的數是1(Beukers (1988))。

它們可以在楊輝三角每橫行從右到左或左到右的第4項找到。

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