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SquaresR[d,n]

gives the number of ways to represent the integer n as a sum of d squares.

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SquaresR

SquaresR[d,n]

gives the number of ways to represent the integer n as a sum of d squares.

Details

  • gives the number of ways to write , where the ni can be positive, negative, or zero.

Examples

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Basic Examples  (3)

Number of ways to represent 45 as a sum of two squares:

The number of integer points on a circle of radius :

Base 2 logarithm of the number of integer points on a sphere of dimension n:

Applications  (2)

Number of lattice points inside the circle of radius 20 with center at the origin:

Approximation of the Sierpiński constant:

Properties & Relations  (4)

The number of representations as the sum of two squares:

PowersRepresentations enumerates the ordered representations up to units:

The ZTransform:

The generating function for SquaresR:

FindSequenceFunction can recognize the SquaresR sequence:

Wolfram Research (2007), SquaresR, Wolfram Language function, https://reference.wolfram.com/language/ref/SquaresR.html.

Text

Wolfram Research (2007), SquaresR, Wolfram Language function, https://reference.wolfram.com/language/ref/SquaresR.html.

CMS

Wolfram Language. 2007. "SquaresR." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SquaresR.html.

APA

Wolfram Language. (2007). SquaresR. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SquaresR.html

BibTeX

@misc{reference.wolfram_2025_squaresr, author="Wolfram Research", title="{SquaresR}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SquaresR.html}", note=[Accessed: 07-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_squaresr, organization={Wolfram Research}, title={SquaresR}, year={2007}, url={https://reference.wolfram.com/language/ref/SquaresR.html}, note=[Accessed: 07-August-2025]}