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 A026802 Number of partitions of n in which the least part is 9. 17
 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 8, 9, 11, 12, 14, 16, 18, 20, 24, 26, 30, 34, 39, 43, 50, 55, 63, 71, 80, 89, 102, 113, 128, 143, 161, 179, 203, 225, 253, 282, 316, 351, 395, 437, 489, 544, 607, 673, 752, 832, 927, 1028, 1143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,27 LINKS FORMULA G.f.: x^9 * Product 1/(1-x^m); m=9..inf. a(n+9)= p(n)-p(n-1)-p(n-2)+p(n-5)+p(n-7)+p(n-9)-p(n-11)-2p(n-12)-p(n-13)-p(n-15)+p(n-16)+p(n-17)+2p(n-18)+p(n-19)+p(n-20)-p(n-21)-p(n-23)-2p(n-24)-p(n-25)+p(n-27)+p(n-29)+p(n-31)-p(n-34)-p(n-35)+p(n-36) where p(n)=A000041(n). [From Shanzhen Gao, Oct 28 2010] a(n) ~ exp(Pi*sqrt(2*n/3)) * 70*Pi^8 / (9*sqrt(3)*n^5). - Vaclav Kotesovec, Jun 02 2018 MATHEMATICA Table[Count[IntegerPartitions[n], _?(Min[#]==9&)], {n, 80}] (* Harvey P. Dale, May 09 2013 *) CROSSREFS 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), A026796 (g=3), A026797 (g=4), A026798 (g=5), A026799 (g=6), A026800 (g=7), A026801 (g=8), this sequence (g=9), A026803 (g=10). Sequence in context: A026827 A025152 * A185329 A029031 A188666 A029156 Adjacent sequences:  A026799 A026800 A026801 * A026803 A026804 A026805 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Arlin Anderson (starship1(AT)gmail.com), Apr 12 2001 STATUS approved

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Last modified December 18 19:04 EST 2018. Contains 318243 sequences. (Running on oeis4.)