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Number of odd integers <= 2^n of form x^2 + y^2.
(Formerly M1077 N0407)
2

%I M1077 N0407 #29 May 01 2022 07:26:15

%S 1,1,2,4,7,13,25,43,83,157,296,564,1083,2077,4006,7733,14968,29044,

%T 56447,109864,214197,418080,816907,1598040,3129063,6132106,12027122,

%U 23606527,46366165,91127332,179207074,352615528,694182554,1367278759

%N Number of odd integers <= 2^n of form x^2 + y^2.

%C First differences of A000050. - _Jean-François Alcover_, Mar 19 2014

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Seth A. Troisi, <a href="/A000074/b000074.txt">Table of n, a(n) for n = 1..50</a>

%H Daniel Shanks, <a href="http://dx.doi.org/10.1090/S0025-5718-1964-0159174-9">The second-order term in the asymptotic expansion of B(x)</a>, Math. Comp., 18 (1964), 75-86.

%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>

%e a(4)=4 since 2^4=16 and 1=1^2, 5=1^2+2^2, 9=3^2, 13=2^2+3^2.

%o (PARI) a(n)=if(n<0,0,sum(k=1,2^(n-1),0<sum(y=0,sqrtint(2*k-1),issquare(2*k-1-y^2))))

%Y Cf. A000050.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E 9 more terms from _Sean A. Irvine_, Sep 14 2009