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A centered heptagonal number is a centered figurate number that represents a heptagon with a dot in the center and all other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for n is given by the formula
- <math>{7n^2 - 7n + 2}\over2<math>.
This can also be calculated by multiplying the triangular number for (n - 1)by 7, then adding 1.
The first few centered heptagonal numbers are
1, 8, 22, 43, 71, 106, 148, 197, 253, 316, 386, 463, 547, 638, 736, 841, 953
Centered heptagonal numbers alternate parity in the pattern odd-even-even-odd.
See also regular heptagonal number.
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