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A002635
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Number of partitions of n into 4 squares.
(Formerly M0053 N0018)
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5
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1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 3, 2, 2, 2, 2, 1, 1, 3, 3, 3, 3, 2, 2, 2, 1, 3, 4, 2, 4, 3, 3, 2, 2, 3, 4, 3, 2, 4, 2, 2, 2, 4, 5, 3, 5, 3, 5, 3, 1, 4, 5, 3, 3, 4, 3, 4, 2, 4, 6, 4, 4, 4, 5, 2, 3, 5, 5, 5, 5, 4, 4, 3, 2, 6, 7, 4, 5, 5, 5, 4, 2, 5, 9, 5, 3, 5, 4, 3, 1, 6, 7, 6, 7, 5, 7, 5, 3, 6, 7, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 84.
D. H. Lehmer, Review of Loria article, Math. Comp. 2 (1947), 301-302.
G. Loria, Sulla scomposizione di un intero nella somma di numeri poligonali. (Italian) Atti Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Nat. (8) 1, (1946). 7-15.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Hirschhorn, M. D.; Some formulae for partitions into squares, DiscreteMath, 211 (2000), pp. 225-228. [From Ant King (mathstutoring(AT)ntlworld.com), Oct 19 2010]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 0..10000
James A. Sellers, Partitions Excluding Specific Polygonal Numbers As Parts, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.
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EXAMPLE
| 1: 1000; 2: 1100; 3:1110; 4: 2000 and 1111; 5: 2100; 6: 2110; 7: 2111; 8: 2200; 9: 3000 and 2210; 10: 3100 and 2211; etc.
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MATHEMATICA
| Length[PowersRepresentations[ #, 4, 2]] & /@ Range[0, 107] [From Ant King (mathstutoring(AT)ntlworld.com), Oct 19 2010]
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PROG
| (PARI) for(n=1, 100, print1(sum(a=0, n, sum(b=0, a, sum(c=0, b, sum(d=0, c, if(a^2+b^2+c^2+d^2-n, 0, 1))))), ", "))
(PARI) a(n)=local(c=0); if(n>=0, forvec(x=vector(4, k, [0, sqrtint(n)]), c+=norml2(x)==n, 1)); c
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CROSSREFS
| Sequence in context: A001876 A033182 A053797 * A108244 A124961 A008967
Adjacent sequences: A002632 A002633 A002634 * A002636 A002637 A002638
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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