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Centered pentagonal number

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Title: Centered pentagonal number  
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Subject: Centered polygonal number, Pentagonal number, 31 (number), 300 (number), Figurate numbers
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Centered pentagonal number

A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for n is given by the formula

{{5n^2 + 5n + 2} \over 2}.

The first few centered pentagonal numbers are

1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 (sequence A005891 in OEIS).

The parity of centered pentagonal numbers follows the pattern even-even-odd-odd, and in base 10 the units follow the pattern 6-6-1-1.

See also

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