cp's OEIS Frontend

A244241 Number of partitions of n into 5 parts such that every i-th smallest part (counted with multiplicity) is different from i.

%I A244241 #11 Jul 28 2025 09:00:06
%S A244241 1,5,11,19,29,39,53,67,84,103,126,150,179,210,246,285,329,376,430,487,
%T A244241 551,619,695,775,864,958,1061,1170,1289,1414,1551,1694,1849,2012,2188,
%U A244241 2372,2570,2777,2999,3231,3479,3737,4013,4300,4605,4923,5260,5610,5981
%N A244241 Number of partitions of n into 5 parts such that every i-th smallest part (counted with multiplicity) is different from i.
%H A244241 Alois P. Heinz, <a href="/A244241/b244241.txt">Table of n, a(n) for n = 20..1000</a>
%H A244241 N. Guru Sharan and Armin Straub, <a href="https://arxiv.org/abs/2507.19047">Partitions with Durfee triangles of fixed size</a>, arXiv:2507.19047 [math.CO], 2025. See p. 5.
%F A244241 Conjectures from _Chai Wah Wu_, Apr 18 2024: (Start)
%F A244241 a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15) for n > 40.
%F A244241 G.f.: x^20*(-x^20 + 2*x^16 + 2*x^15 + 4*x^14 + x^13 - 3*x^12 - 7*x^11 - 9*x^10 - 5*x^9 + 2*x^8 + 8*x^7 + 9*x^6 + 8*x^5 + x^4 - 3*x^3 - 5*x^2 - 4*x - 1)/((x - 1)^5*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)
%Y A244241 Column k=5 of A238406.
%K A244241 nonn
%O A244241 20,2
%A A244241 _Alois P. Heinz_, Jun 23 2014