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A265093 a(n) = Sum_{k=0..n} q(k)^2, where q(k) = partition numbers into distinct parts (A000009). 3
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 (list; graph; refs; listen; history; text; internal format)
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: A160434 A139630 A245738 * A133044 A014529 A095015

Adjacent sequences:  A265090 A265091 A265092 * A265094 A265095 A265096

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 01 2015

STATUS

approved

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Last modified February 26 05:46 EST 2020. Contains 332276 sequences. (Running on oeis4.)