cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A072243 Number of distinct partitions of n^2.

This page as a plain text file.
%I A072243 #14 Apr 10 2017 11:52:06
%S A072243 1,1,2,8,32,142,668,3264,16444,84756,444793,2368800,12769602,69545358,
%T A072243 382075868,2114965120,11784471548,66043042088,372022512608,
%U A072243 2105220502772,11962163400706,68223286792200,390406746862530,2240962117491470,12899456450932840
%N A072243 Number of distinct partitions of n^2.
%H A072243 Vaclav Kotesovec, <a href="/A072243/b072243.txt">Table of n, a(n) for n = 0..1260</a> (terms 0..200 from Alois P. Heinz)
%F A072243 a(n) ~ exp(Pi*n/sqrt(3)) / (4*3^(1/4)*n^(3/2)). - _Vaclav Kotesovec_, Dec 01 2015
%F A072243 a(n) = A000009(A000290(n)). - _Alois P. Heinz_, Jan 22 2017
%p A072243 with(numtheory):
%p A072243 b:= proc(n) option remember; `if`(n=0, 1, add(add(
%p A072243       `if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
%p A072243     end:
%p A072243 a:= n-> b(n^2):
%p A072243 seq(a(n), n=0..30);  # _Alois P. Heinz_, Jan 22 2017
%t A072243 Table[ PartitionsQ[n^2], {n, 1, 24}]
%Y A072243 Cf. A000009, A000041, A000290, A072213, A281489.
%K A072243 nonn
%O A072243 0,3
%A A072243 _Robert G. Wilson v_, Jul 06 2002
%E A072243 a(0)=1 prepended by _Alois P. Heinz_, Jan 22 2017