A248334 The subsequence of A246885 having even values.

0, 2, 4, 6, 16, 20, 32, 34, 48, 54, 58, 86, 108, 110, 124, 128, 132, 160, 162, 236, 250, 254, 256, 258, 272, 282, 310, 358, 384, 432, 436, 464, 500, 502, 506, 516, 540, 554, 628, 686, 688, 690, 718, 750, 794, 864, 866, 880, 918, 932, 942, 992, 1024, 1028, 1056

Offset: 1

Author

David S. Newman, Oct 04 2014

Keywords

• nonn

Comments

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.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Joshua N. Cooper, Dennis Eichhorn, Kevin O'Bryant, Reciprocals of Binary Power Series, arXiv:math/0506496 [math.NT], 2005.

Programs

Maple

b:= proc(n) option remember; irem(`if`(n=0, 1,
      `if`(n<0, 0, add(b(n-i^3), i=1..iroot(n, 3)))), 2)
    end:
a:= proc(n) option remember; local k; for k from 2+
      `if`(n=1, -2, a(n-1)) by 2 while b(k)=0 do od; k
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Dec 28 2014

Mathematica

InverseOfCubes[m_]:=Module[{V},V[0]=1;Do[V[i]=0,{i,1,m}];
Reap[Sow[0];
Do[If[OddQ[Sum[V[counter-i^3],{i,1,counter^(1/3)}]],V[counter]=1;
Sow[counter]],{counter,1,m}]][[2,1]]]
inv=InverseOfCubes[400];
Select[inv,EvenQ]
(* This program adapted from code written by Kevin O'Bryant *)

Extensions

More terms from Alois P. Heinz, Dec 28 2014