A031124 Expansion of (1+z)/(1-z) - 2*Sum_{m>=1} z^(m^2)/(1-z^((m+1)^2)).

1, 0, 2, 2, 0, 0, 2, 2, 2, -2, 2, 2, 2, -2, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, -4, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, -4, 2, 2, 2, 0, 2, 2, 2, -4, 2, 2, 2, 0, 2, 2, 2, -2, 0, 2, 2, -2, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 2, -2, 2, 2, 0, 0, 2, 2

Offset

0,3

Links

Table of n, a(n) for n=0..79.

N. Luzin, Function: Part II, Amer. Math. Monthly, 105 (1998), 263-270.

Mathematica

nmax = 100; CoefficientList[Series[(1+x)/(1-x) - 2*Sum[x^(m^2)/(1 - x^((m+1)^2)), {m, 1, Floor[Sqrt[nmax]] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Oct 04 2017 *)

Prog

(PARI) lista(nn) = Vec((1+z)/(1-z) - 2*sum(m=1, nn, z^(m^2)/(1-z^((m+1)^2) + O(z^nn)))); \\ Michel Marcus, Oct 02 2017

Crossrefs

Cf. A031123.

Sequence in context: A039972 A344834 A344837 * A063695 A081417 A133388

Adjacent sequences: A031121 A031122 A031123 * A031125 A031126 A031127

Keyword

sign

Author

N. J. A. Sloane

Status

approved