A246885 Those n for which the coefficients of x^n in the reciprocal of 1+x+x^8+...+x^(i^3)+... are odd.

0, 1, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 16, 19, 20, 23, 29, 32, 34, 35, 37, 45, 47, 48, 49, 53, 54, 57, 58, 67, 69, 71, 73, 75, 85, 86, 99, 101, 107, 108, 109, 110, 115, 121, 123, 124, 127, 128, 129, 131, 132, 135, 137, 141, 143, 155, 157, 160, 161, 162, 163, 169, 177, 183, 189, 193, 195, 197, 199, 203

Offset: 1

Author

David S. Newman, Sep 06 2014

Keywords

• nonn

Comments

Numbers n such that the number of compositions of n into cubes (A023358) is odd. - Joerg Arndt, Sep 08 2014

Examples

			The reciprocal of 1+x+x^8+x^27+... begins 1 -x +x^2 -x^3 +x^4 -x^5 +x^6 -x^7 +x^9 -2*x^10 +...  So the first few values of a(n) are 0,1,2,3,4,5,6,7,9... .
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• J. N. Cooper, D. Eichhorn and K. O'Bryant, Reciprocals of binary power series, arXiv:math/0506496 [math.NT], 2005.

Crossrefs

Cf. A023358.

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 1+
      `if`(n=1, -1, a(n-1)) while b(k)=0 do od; k
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Sep 08 2014

Mathematica

iend=10;
seq=Flatten[Position[Delete[Mod[CoefficientList[Series[1/Sum[x^(i^3),{i,0,iend}],{x,0,iend^3}],x],2],1],1]];
Print[seq];