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

1,2

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.

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 *)

Crossrefs

Sequence in context: A330359 A000068 A067662 * A001774 A053285 A286850

Adjacent sequences: A248331 A248332 A248333 * A248335 A248336 A248337

Keyword

nonn

Author

David S. Newman, Oct 04 2014

Extensions

More terms from Alois P. Heinz, Dec 28 2014

Status

approved