Search: id:A000161
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%I A000161
%S A000161 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,
%T A000161 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,
%U A000161 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
%N A000161 Number of partitions of n into 2 squares.
%C A000161 Number of ways of writing n as a sum of 2 squares when order does not 
               matter.
%C A000161 Number of similar sublattices of square lattice with index n.
%D A000161 E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, 
               NY, 1985, p. 84.
%D A000161 J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, 
               NY, 1939, p. 339
%H A000161 T. D. Noe, <a href="b000161.txt">Table of n, a(n) for n = 0..10000</a>
%H A000161 H. Bottomley, <a href="a001481.gif">Illustration of initial terms</a>
%H A000161 R. T. Bumby, <a href="http://www.math.rutgers.edu/~bumby/squares1.pdf">
               Sums of four squares</a>, in Number theory (New York, 1991-1995), 
               1-8, Springer, New York, 1996.
%H A000161 J. H. Conway, E. M. Rains and N. J. A. Sloane, On the existence of similar 
               sublattices, Canad. J. Math. 51 (1999), 1300-1306 (<a href="http:/
               /www.research.att.com/~njas/doc/sim.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/sim.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/sim.ps">ps</a>).
%H A000161 Michael Gilleland, <a href="selfsimilar.html">Some Self-Similar Integer 
               Sequences</a>
%H A000161 <a href="Sindx_Su.html#sublatts">Index entries for sequences related 
               to sublattices</a>
%H A000161 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%H A000161 <a href="Sindx_Cor.html#core">Index entries for "core" sequences</a>
%F A000161 a(n) = card { { a,b } c N | a^2+b^2 = n } - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Nov 23 2007
%e A000161 25 = 3^2+4^2 = 5^2, so a(25) = 2.
%p A000161 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) ];
%p A000161 A000161 := n -> nops( numtheory[sum2sqr](n) ); - M. F. Hasler (Maximilian.Hasler(AT)gmail.com), 
               Nov 23 2007
%o A000161 (PARI) A000161(n)=sum(i=0,n,sum(j=0,i,if(i^2+j^2-n,0,1)))
%o A000161 (PARI) A000161(n)=sum(i=0,sqrtint(n>>1),issquare(n-i^2)) - M. F. Hasler 
               (Maximilian.Hasler(AT)gmail.com), Nov 23 2007
%Y A000161 Cf. A002654, A001481.
%Y A000161 Sequence in context: A056973 A107782 A086017 this_sequence A060398 A122855 
               A140727
%Y A000161 Adjacent sequences: A000158 A000159 A000160 this_sequence A000162 A000163 
               A000164
%K A000161 nonn,core,easy,nice
%O A000161 0,26
%A A000161 N. J. A. Sloane (njas(AT)research.att.com).

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