|
%I #16 Sep 08 2014 08:09:39
%S 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,
%T 54,57,58,67,69,71,73,75,85,86,99,101,107,108,109,110,115,121,123,124,
%U 127,128,129,131,132,135,137,141,143,155,157,160,161,162,163,169,177,183,189,193,195,197,199,203
%N Those n for which the coefficients of x^n in the reciprocal of 1+x+x^8+...+x^(i^3)+... are odd.
%C Numbers n such that the number of compositions of n into cubes (A023358) is odd. - _Joerg Arndt_, Sep 08 2014
%H Alois P. Heinz, <a href="/A246885/b246885.txt">Table of n, a(n) for n = 1..10000</a>
%H J. N. Cooper, D. Eichhorn and K. O'Bryant, <a href="http://arXiv.org/abs/math.NT/0506496">Reciprocals of binary power series</a>, arXiv:math/0506496 [math.NT], 2005.
%e 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... .
%p b:= proc(n) option remember; irem(`if`(n=0, 1,
%p `if`(n<0, 0, add(b(n-i^3), i=1..iroot(n, 3)))), 2)
%p end:
%p a:= proc(n) option remember; local k; for k from 1+
%p `if`(n=1, -1, a(n-1)) while b(k)=0 do od; k
%p end:
%p seq(a(n), n=1..80); # _Alois P. Heinz_, Sep 08 2014
%t iend=10;
%t seq=Flatten[Position[Delete[Mod[CoefficientList[Series[1/Sum[x^(i^3),{i,0,iend}],{x,0,iend^3}],x],2],1],1]];
%t Print[seq];
%Y Cf. A023358.
%K nonn
%O 1,3
%A _David S. Newman_, Sep 06 2014
|
