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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

Table of n, a(n) for n=1..79.

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g

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]

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

Clark Kimberling

EXTENSIONS

More terms from Arlin Anderson (starship1(AT)gmail.com), Apr 12 2001

STATUS

approved

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Last modified May 23 23:53 EDT 2017. Contains 286937 sequences.