A265093 a(n) = Sum_{k=0..n} q(k)^2, where q(k) = partition numbers into distinct parts (A000009).

1, 2, 3, 7, 11, 20, 36, 61, 97, 161, 261, 405, 630, 954, 1438, 2167, 3191, 4635, 6751, 9667, 13763, 19539, 27460, 38276, 53160, 73324, 100549, 137413, 186697, 252233, 339849, 455449, 607549, 808253, 1070397, 1412622, 1858846, 2436446, 3182942, 4147266

Offset

0,2

Comments

In general, for m >= 1, Sum_{k=0..n} q(k)^m ~ 2*sqrt(3*n)/(m*Pi) * q(n)^m ~ exp(Pi*m*sqrt(n/3)) / (Pi*m * 2^(2*m-1) * 3^(m/4-1/2) * n^(3*m/4-1/2)), where q(k) is A000009(k).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{k=0..n} A000009(k)^2.

a(n) ~ exp(2*Pi*sqrt(n/3))/(16*Pi*n).

Mathematica

Table[Sum[PartitionsQ[k]^2, {k, 0, n}], {n, 0, 50}]

Crossrefs

Cf. A000070, A036469, A259399.

Sequence in context: A139630 A245738 A368032 * A133044 A014529 A095015

Adjacent sequences: A265090 A265091 A265092 * A265094 A265095 A265096

Keyword

nonn

Author

Vaclav Kotesovec, Dec 01 2015

Status

approved