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A248334 The subsequence of A246885 having even values.

%I A248334 #19 Dec 28 2014 23:05:29
%S A248334 0,2,4,6,16,20,32,34,48,54,58,86,108,110,124,128,132,160,162,236,250,
%T A248334 254,256,258,272,282,310,358,384,432,436,464,500,502,506,516,540,554,
%U A248334 628,686,688,690,718,750,794,864,866,880,918,932,942,992,1024,1028,1056
%N A248334 The subsequence of A246885 having even values.
%C A248334 Let f(x)=Sum(x^i^3), then 1/f(x) has coefficients given in A246885. The subsequence of A246885 having even values is A248334. This is the same as the numbers that can be written in an odd number of ways as a sum 2r^3 + 4s^3, where r and s are nonnegative integers.
%H A248334 Alois P. Heinz, <a href="/A248334/b248334.txt">Table of n, a(n) for n = 1..10000</a>
%H A248334 Joshua N. Cooper, Dennis Eichhorn, Kevin O'Bryant, <a href="http://arxiv.org/abs/math/0506496">Reciprocals of Binary Power Series</a>, arXiv:math/0506496 [math.NT], 2005.
%p A248334 b:= proc(n) option remember; irem(`if`(n=0, 1,
%p A248334       `if`(n<0, 0, add(b(n-i^3), i=1..iroot(n, 3)))), 2)
%p A248334     end:
%p A248334 a:= proc(n) option remember; local k; for k from 2+
%p A248334       `if`(n=1, -2, a(n-1)) by 2 while b(k)=0 do od; k
%p A248334     end:
%p A248334 seq(a(n), n=1..80);  # _Alois P. Heinz_, Dec 28 2014
%t A248334 InverseOfCubes[m_]:=Module[{V},V[0]=1;Do[V[i]=0,{i,1,m}];
%t A248334 Reap[Sow[0];
%t A248334 Do[If[OddQ[Sum[V[counter-i^3],{i,1,counter^(1/3)}]],V[counter]=1;
%t A248334 Sow[counter]],{counter,1,m}]][[2,1]]]
%t A248334 inv=InverseOfCubes[400];
%t A248334 Select[inv,EvenQ]
%t A248334 (* This program adapted from code written by Kevin O'Bryant *)
%K A248334 nonn
%O A248334 1,2
%A A248334 _David S. Newman_, Oct 04 2014
%E A248334 More terms from _Alois P. Heinz_, Dec 28 2014