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%I #23 Sep 08 2022 08:45:46
%S 1,0,1,1,1,1,3,1,3,4,4,4,8,6,10,11,13,15,22,20,28,33,39,43,58,60,77,
%T 88,104,119,148,160,197,226,265,300,363,404,481,549,638,727,858,961,
%U 1126,1283,1480,1680,1953,2201,2544,2887,3309,3750,4312,4857,5566,6301,7175
%N a(n) = A053445(n-2) - A053445(n-4).
%C a(n) counts partitions of n such that all parts are >=2 and the largest part occurs at least three times, see example.
%H Andrew van den Hoeven, <a href="/A162932/b162932.txt">Table of n, a(n) for n = 6..10000</a>
%F From _Mircea Merca_, Jun 11 2012: (Start)
%F a(n) = p(n)-2*p(n-1)+2*p(n-3)-p(n-4), where p(n) = A000041(n).
%F G.f.: (1-x)*Product_{k>2} 1/(1-x^k). (End)
%F a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (36*sqrt(2)*n^(5/2)). - _Vaclav Kotesovec_, Jun 02 2018
%e For n = 19 the a(19)=6 partitions are 5554, 44443, 55522, 444322, 3333322, and 33322222.
%t Table[PartitionsP[n] - 2 PartitionsP[n - 1] + 2 PartitionsP[n - 3] - PartitionsP[n - 4], {n, 6, 70}] (* _Vincenzo Librandi_, Dec 09 2014 *)
%o (Magma) a:=func<n | NumberOfPartitions(n)-2*NumberOfPartitions(n-1)+2*NumberOfPartitions(n-3)-NumberOfPartitions(n-4)>; [a(n): n in [6..100]]; // _Vincenzo Librandi_, Dec 09 2014
%Y Cf. A162931, A079946.
%K nonn
%O 6,7
%A _Alford Arnold_, Jul 17 2009
%E Keyword:tabf removed, indexing corrected, sequence extended by _R. J. Mathar_, Sep 17 2009
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