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Pentagonal Pyramidal Number

Definition

A figurate number corresponding to a pentagonal pyramid. The first few are 1, 6, 18, 40, 75, ... (OEIS A002411). The generating function for the pentagonal pyramidal numbers is (x(2x + 1))/(x - 1)^4 = x + 6x^2 + 18x^3 + 40x^4 + .... The odd pentagonal pyramidal numbers are given by 1, 75, 405, 1183, 2601, ... (OEIS A015223), having squares 1, 5625, 164025, ... (OEIS A014799), while the even pentagonal pyramidal numbers are given by 6, 18, 40, 126, 196, 288, ... (OEIS A015224), having squares 36, 324, 1600, 15876, ... (OEIS A014800).

Related terms

pentagonal number | pyramidal number

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