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 A026796 Number of partitions of n in which the least part is 3. 26
 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 9, 10, 13, 17, 21, 25, 33, 39, 49, 60, 73, 88, 110, 130, 158, 191, 230, 273, 331, 391, 468, 556, 660, 779, 927, 1087, 1284, 1510, 1775, 2075, 2438, 2842, 3323, 3872, 4510, 5237, 6095, 7056, 8182, 9465, 10945, 12625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Let b(k) be the number of partitions of k for which twice the number of ones is the number of parts, k = 0, 1, 2, ... . Then a(n+4) = b(n), n = 0, 1, 2, ... (conjectured). - George Beck, Aug 19 2017 LINKS FORMULA G.f.: x^3 / Product_{m>=3} (1 - x^m). a(n) = p(n-3) - p(n-4) - p(n-5) + p(n-6), where p(n) = A000041(n). - Bob Selcoe, Aug 07 2014 a(n) ~ exp(Pi*sqrt(2*n/3)) * Pi^2 / (12*sqrt(3)*n^2). - Vaclav Kotesovec, Jun 02 2018 MATHEMATICA Table[Count[IntegerPartitions[n],   p_ /; Min@p==3], {n, 0, 56}] (* George Beck Aug 19 2017 *) PROG (PARI) a(n) = numbpart(n-3) - numbpart(n-4) - numbpart(n-5) + numbpart(n-6); \\ Michel Marcus, Aug 20 2014 (PARI) x='x+O('x^66); Vecrev(Pol(x^3*(1-x)*(1-x^2)/eta(x))) \\ Joerg Arndt, Aug 22 2014 CROSSREFS Essentially the same sequence as A008483. Not necessarily connected 2-regular graphs with girth at least g [partitions into parts >= g]: A026807 (triangle); chosen g: A000041 (g=1 -- multigraphs with loops allowed), A002865 (g=2 -- multigraphs with loops forbidden), A008483 (g=3), A008484 (g=4), A185325(g=5), A185326 (g=6), A185327 (g=7), A185328 (g=8), A185329 (g=9). Not necessarily connected 2-regular graphs with girth exactly g [partitions with smallest part g]: A026794 (triangle); chosen g: A002865 (g=2 -- multigraphs with at least one pair of parallel edges, but loops forbidden), this sequence (g=3), A026797 (g=4), A026798 (g=5), A026799 (g=6), A026800 (g=7), A026801 (g=8), A026802 (g=9), A026803 (g=10). Not necessarily connected k-regular simple graphs girth exactly 3: A198313 (any k), A185643 (triangle); fixed k: this sequence (k=2), A185133 (k=3), A185143 (k=4), A185153 (k=5), A185163 (k=6). Sequence in context: A027195 A008483 A281356 * A008925 A266749 A238625 Adjacent sequences:  A026793 A026794 A026795 * A026797 A026798 A026799 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Michel Marcus, Aug 20 2014 a(0) = 0 prepended by Joerg Arndt, Aug 22 2014 STATUS approved

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Last modified November 20 09:08 EST 2018. Contains 317385 sequences. (Running on oeis4.)