cp's OEIS Frontend

A220479 Total number of smallest parts that are also emergent parts in all partitions of n.

%I A220479 #23 Jun 05 2021 16:33:44
%S A220479 0,0,0,1,0,3,1,5,5,10,8,22,19,33,40,62,67,107,118,175,208,282,331,462,
%T A220479 542,712,859,1112,1323,1709,2030,2568,3078,3830,4577,5687,6760,8291,
%U A220479 9885,12045,14290,17334,20515,24710,29242,35004,41282,49283,57963,68836
%N A220479 Total number of smallest parts that are also emergent parts in all partitions of n.
%C A220479 For the definition of emergent parts see A182699.
%H A220479 Vaclav Kotesovec, <a href="/A220479/b220479.txt">Table of n, a(n) for n = 1..1000</a>
%F A220479 a(n) = A092269(n) - A000070(n-1) - A002865(n) = A092269(n) - A120452(n+1) = A195820(n) - A002865(n).
%F A220479 a(n) = A092269(n) - A000041(n) - A000070(n-2), n >= 2.
%F A220479 a(n) = A215513(n) - A000070(n-2), n >= 2.
%F A220479 a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*sqrt(3)*n). - _Vaclav Kotesovec_, Jul 31 2017
%t A220479 b[n_, i_] := b[n, i] = If[n==0 || i==1, n, {q, r} = QuotientRemainder[n, i]; If[r==0, q, 0] + Sum[b[n-i*j, i-1], {j, 0, n/i}]];
%t A220479 c[n_] := b[n, n];
%t A220479 d[n_] := Total[PartitionsP[Range[0, n-3]]] + PartitionsP[n-1];
%t A220479 a[n_] := c[n] - d[n+1];
%t A220479 Array[a, 50] (* _Jean-François Alcover_, Jun 05 2021, using _Alois P. Heinz_'s code for A092269 *)
%Y A220479 Cf. A000041, A000070, A002865, A006128, A092269, A120452, A182699, A182709, A195820, A206437, A215513.
%K A220479 nonn
%O A220479 1,6
%A A220479 _Omar E. Pol_, Jan 12 2013
%E A220479 a(43) corrected by _Vaclav Kotesovec_, Jul 31 2017