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Search: id:A000144
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| A000144 |
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Number of ways of writing n as a sum of 10 squares. |
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+0
2
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| 1, 20, 180, 960, 3380, 8424, 16320, 28800, 52020, 88660, 129064, 175680, 262080, 386920, 489600, 600960, 840500, 1137960, 1330420, 1563840, 2050344, 2611200, 2986560, 3358080, 4194240, 5318268, 5878440, 6299520, 7862400, 9619560
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 121.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 314.
G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Chelsea Publishing Company, New York 1959, p. 135 section 9.3. MR0106147 (21 #4881)
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares
Index entries for sequences related to sums of squares
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FORMULA
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Euler transform of period 4 sequence [20, -30, 20, -10, ...]. - Michael Somos Sep 12 2005
Expansion of eta(q^2)^50/(eta(q)eta(q^4))^20 in powers of q. - Michael Somos Sep 12 2005
a(n)=4/5*(A050456(n)+16*A050468(n)+8*A030212(n)) if n>0. - Michael Somos Sepe 12 2005
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MAPLE
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(sum(x^(m^2), m=-10..10))^10;
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MATHEMATICA
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Needs["NumberTheory`NumberTheoryFunctions`"]; Table[SumOfSquaresR[10, n], {n, 0, 30}] (*Chandler*)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^10, n)) /* Michael Somos Sep 12 2005 */
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CROSSREFS
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Sequence in context: A159538 A091983 A037250 this_sequence A047645 A010936 A014806
Adjacent sequences: A000141 A000142 A000143 this_sequence A000145 A000146 A000147
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 28 2006
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