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 A162932 a(n) = A053445(n-2) - A053445(n-4). 4
 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, 88, 104, 119, 148, 160, 197, 226, 265, 300, 363, 404, 481, 549, 638, 727, 858, 961, 1126, 1283, 1480, 1680, 1953, 2201, 2544, 2887, 3309, 3750, 4312, 4857, 5566, 6301, 7175 (list; graph; refs; listen; history; text; internal format)
 OFFSET 6,7 COMMENTS a(n) counts partitions of n such that all parts are >=2 and the largest part occurs at least three times, see example. LINKS Andrew van den Hoeven, Table of n, a(n) for n = 6..10000 FORMULA From Mircea Merca, Jun 11 2012: (Start) a(n) = p(n)-2*p(n-1)+2*p(n-3)-p(n-4), where p(n) = A000041(n). G.f.: (1-x)*Product_{k>2} 1/(1-x^k). (End) a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^3 / (36*sqrt(2)*n^(5/2)). - Vaclav Kotesovec, Jun 02 2018 EXAMPLE For n = 19 the a(19)=6 partitions are 5554, 44443, 55522, 444322, 3333322, and 33322222. MATHEMATICA Table[PartitionsP[n] - 2 PartitionsP[n - 1] + 2 PartitionsP[n - 3] - PartitionsP[n - 4], {n, 6, 70}] (* Vincenzo Librandi, Dec 09 2014 *) PROG (Magma) a:=func; [a(n): n in [6..100]]; // Vincenzo Librandi, Dec 09 2014 CROSSREFS Cf. A162931, A079946. Sequence in context: A320279 A175290 A089958 * A216036 A008924 A175186 Adjacent sequences: A162929 A162930 A162931 * A162933 A162934 A162935 KEYWORD nonn AUTHOR Alford Arnold, Jul 17 2009 EXTENSIONS Keyword:tabf removed, indexing corrected, sequence extended by R. J. Mathar, Sep 17 2009 STATUS approved

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Last modified August 10 21:39 EDT 2024. Contains 375058 sequences. (Running on oeis4.)