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Search: id:A000161
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| A000161 |
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Number of partitions of n into 2 squares. |
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+0
20
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| 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0
(list; graph; listen)
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OFFSET
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0,26
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COMMENT
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Number of ways of writing n as a sum of 2 squares when order does not matter.
Number of similar sublattices of square lattice with index n.
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REFERENCES
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E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, p. 84.
J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, p. 339
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..10000
H. Bottomley, Illustration of initial terms
R. T. Bumby, Sums of four squares, in Number theory (New York, 1991-1995), 1-8, Springer, New York, 1996.
J. H. Conway, E. M. Rains and N. J. A. Sloane, On the existence of similar sublattices, Canad. J. Math. 51 (1999), 1300-1306 (Abstract, pdf, ps).
Michael Gilleland, Some Self-Similar Integer Sequences
Index entries for sequences related to sublattices
Index entries for sequences related to sums of squares
Index entries for "core" sequences
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FORMULA
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a(n) = card { { a,b } c N | a^2+b^2 = n } - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 23 2007
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EXAMPLE
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25 = 3^2+4^2 = 5^2, so a(25) = 2.
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MAPLE
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A000161 := proc(n) local i, j, ans; ans := 0; for i from 0 to n do for j from i to n do if i^2+j^2=n then ans := ans+1 fi od od; RETURN(ans); end; [ seq(A000161(i), i=0..50) ];
A000161 := n -> nops( numtheory[sum2sqr](n) ); - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 23 2007
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PROGRAM
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(PARI) A000161(n)=sum(i=0, n, sum(j=0, i, if(i^2+j^2-n, 0, 1)))
(PARI) A000161(n)=sum(i=0, sqrtint(n>>1), issquare(n-i^2)) - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Nov 23 2007
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CROSSREFS
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Cf. A002654, A001481.
Sequence in context: A056973 A107782 A086017 this_sequence A060398 A122855 A140727
Adjacent sequences: A000158 A000159 A000160 this_sequence A000162 A000163 A000164
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KEYWORD
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nonn,core,easy,nice
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AUTHOR
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njas
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