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Centered Triangular Number

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CenteredTriangularNumber

A centered triangular number is a centered polygonal number consisting of a central dot with three dots around it, and then additional dots in the gaps between adjacent dots. The nth term is (3n^2+3n+2)/2, and the first few such numbers for n=0, 1, 2, ... are 1, 4, 10, 19, 31, 46, 64, ... (OEIS A005448). The generating function giving the centered triangular numbers is

(x^2+x+1)/((1-x)^3)=1+4x+10x^2+19x^3+....

See also

Centered Pentagonal Number, Centered Polygonal Number, Centered Square Number, Hex Number, Triangular Number

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References

Sloane, N. J. A. Sequence A005448/M3378 in "The On-Line Encyclopedia of Integer Sequences."

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Centered Triangular Number

Cite this as:

Weisstein, Eric W. "Centered Triangular Number." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CenteredTriangularNumber.html

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