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 A026801 Number of partitions of n in which the least part is 8. 17
 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 7, 7, 9, 10, 12, 13, 16, 17, 21, 23, 27, 30, 36, 39, 46, 51, 60, 66, 77, 85, 99, 110, 126, 140, 162, 179, 205, 228, 260, 289, 329, 365, 415, 461, 521, 579, 655, 726, 818, 909, 1022, 1134, 1273, 1411 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,24 LINKS FORMULA G.f.: x^8 * Product 1/(1-x^m); m=8..inf. a(n+8) = p(n)-p(n-1)-p(n-2)+p(n-5)+p(n-7)+p(n-8)-p(n-10)-p(n-11)-2p(n-12)+2p(n-16)+p(n-17)+p(n-18)-p(n-20)-p(n-21)-p(n-23)+p(n-26)+p(n-27)-p(n-28) where p(n)=A000041(n). [From Shanzhen Gao, Oct 28 2010] a(n) ~ exp(Pi*sqrt(2*n/3)) * 35*Pi^7 / (18*sqrt(2)*n^(9/2)). - Vaclav Kotesovec, Jun 02 2018 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), this sequence (g=8), A026802 (g=9), A026803 (g=10). Sequence in context: A026826 A025151 * A185328 A210718 A027191 A122522 Adjacent sequences:  A026798 A026799 A026800 * A026802 A026803 A026804 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 November 14 15:00 EST 2018. Contains 317208 sequences. (Running on oeis4.)