Search: id:A000021
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%I A000021 M0357 N0134
%S A000021 1,1,2,2,6,9,17,30,54,98,183,341,645,1220,2327,4451,8555,16489,31859,61717,
%T A000021 119779,232919,453584,884544,1727213,3376505,6607371,12942012,25371540,
               49777187,
%U A000021 97731027,192010355,377475336,742512992,1461352025,2877572478,5668965407
%N A000021 Number of positive integers <= 2^n of form x^2 + 12 y^2.
%D A000021 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000021 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000021 D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, 
               Math. Comp., 20 (1966), 551-569.
%H A000021 <a href="Sindx_Qua.html#quadpop">Index entries for sequences related 
               to populations of quadratic forms</a>
%e A000021 a(4)=6 since 2^4=16 and 1=1^2, 4=2^2, 9=3^2, 12=12*1^2, 13=1^2+12*1^2, 
               16=4^2.
%o A000021 (PARI) a(n)=if(n<0,0,sum(k=1,2^n,0<sum(y=0,sqrtint(k\12),issquare(k-12*y^2))))
%o A000021 (PARI) a(n)=local(A);if(n<0,0,A=qfrep([1,0;0,12],2^n);sum(k=1,2^n,A[k]!=0))
%Y A000021 Sequence in context: A131553 A094485 A021819 this_sequence A000022 A034805 
               A051765
%Y A000021 Adjacent sequences: A000018 A000019 A000020 this_sequence A000022 A000023 
               A000024
%K A000021 nonn
%O A000021 0,3
%A A000021 N. J. A. Sloane (njas(AT)research.att.com).
%E A000021 More terms from David W. Wilson (davidwwilson(AT)comcast.net), Feb 07 
               2000.

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