A246885 - OEIS

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

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OFFSET

1,3

COMMENTS

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

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.

EXAMPLE

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... .

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];