login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=1..75.

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

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]

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

Clark Kimberling

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 20:48 EST 2017. Contains 295856 sequences.