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A000132 Number of ways of writing n as a sum of 5 squares. 12
1, 10, 40, 80, 90, 112, 240, 320, 200, 250, 560, 560, 400, 560, 800, 960, 730, 480, 1240, 1520, 752, 1120, 1840, 1600, 1200, 1210, 2000, 2240, 1600, 1680, 2720, 3200, 1480, 1440, 3680, 3040, 2250, 2800, 3280, 4160, 2800, 1920, 4320, 5040, 2800, 3472, 5920 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The units digit of a(n) is 2 if n=5*t^2 for some natural number t, and 0 otherwise. See Moreno & Wagstaff, p.258 exercise 2. - Ant King, Mar 17 2013

See A025429 for the number of partitions of n into five nonzero squares. - M. F. Hasler, May 30 2014

REFERENCES

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 128.

J. Carlos Moreno and Samuel S. Wagstaff Jr., Sums Of Squares Of Integers, Chapman & Hall/CRC, (2006). [Ant King Mar, 17 2013]

LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000

Shi-Chao Chen, Congruences for rs(n), Journal of Number Theory, Volume 130, Issue 9, September 2010, Pages 2028-2032.

S. Cooper, Sums of five, seven and nine squares, Ramanujan J., vol 6, no. 4, (2002) 469-490.

S. C. Milne, Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions and Schur functions, Ramanujan J., 6 (2002), 7-149.

Index entries for sequences related to sums of squares

FORMULA

G.f.: sum(j=-inf..+inf, x^(j^2) )^5. - R. J. Mathar, Jul 31 2007

a(n) = (10/n)*Sum_{k=1..n} A186690(k)*a(n-k), a(0) = 1. - Seiichi Manyama, May 27 2017

EXAMPLE

G.f. = 1 + 10*x + 40*x^2 + 80*x^3 + 90*x^4 + 112*x^5 + 240*x^6 + ...

MATHEMATICA

Table[SquaresR[5, n], {n, 0, 46}] (* Ray Chandler, Nov 28 2006 *)

SquaresR[5, Range[0, 50]] (* Harvey P. Dale, Aug 26 2011 *)

PROG

(Sage)

Q = DiagonalQuadraticForm(ZZ, [1]*5)

Q.representation_number_list(47) # Peter Luschny, Jun 20 2014

CROSSREFS

5th column of A286815. - Seiichi Manyama, May 27 2017

Row d=5 of A122141.

Cf. A025429.

Sequence in context: A104045 A102546 A108777 * A217073 A210376 A060317

Adjacent sequences:  A000129 A000130 A000131 * A000133 A000134 A000135

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Extended by Ray Chandler, Nov 28 2006

STATUS

approved

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Last modified July 26 08:41 EDT 2017. Contains 289800 sequences.