Centered pentagonal number

From Academic Kids

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

<math>{{(5n^2 + 5n + 2)} \over 2}<math>.

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

The parity of centered pentagonal numbers follows the pattern even-even-odd-odd, and in base 10 one can notice the one's digits follows the pattern 6-6-1-1.

See also

polygonal number

pentagonal number

External links

Centered Pentagonal Number -- from MathWorld (http://mathworld.wolfram.com/CenteredPentagonalNumber.html|)

fr:Nombre pentagonal centré

it:Numero pentagonale centrato

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