The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A185328 Number of partitions of n with parts >= 8. 20
 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 0,17 COMMENTS a(n) is also the number of not necessarily connected 2-regular graphs on n-vertices with girth at least 8 (all such graphs are simple). The integer i corresponds to the i-cycle; addition of integers corresponds to disconnected union of cycles. By removing a single part of size 8, an A026801 partition of n becomes an A185328 partition of n - 8. Hence this sequence is essentially the same as A026801. LINKS Robert Israel, Table of n, a(n) for n = 0..2000 FORMULA G.f.: Product_{m>=8} 1/(1-x^m). a(n) = p(n) - p(n-1) - p(n-2) + p(n-5) + p(n-7) + p(n-8) - p(n-10) - p(n-11) - 2*p(n-12) + 2*p(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). - Shanzhen Gao This sequence is the Euler transformation of A185118. a(n) ~ exp(Pi*sqrt(2*n/3)) * 35*Pi^7 / (18*sqrt(2)*n^(9/2)). - Vaclav Kotesovec, Jun 02 2018 G.f.: Sum_{k>=0} x^(8*k) / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Nov 28 2020 MAPLE N:= 100: # for a(0)..a(N) g:= mul(1/(1-x^m), m=8..N): S:= series(g, x, N+1): seq(coeff(S, x, n), n=0..N); # Robert Israel, Dec 19 2017 MATHEMATICA CoefficientList[Series[1/QPochhammer[x^8, x], {x, 0, 75}], x] (* G. C. Greubel, Nov 03 2019 *) PROG (PARI) my(x='x+O('x^70)); Vec(1/prod(m=0, 80, 1-x^(m+8))) \\ G. C. Greubel, Nov 03 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/(&*[1-x^(m+8): m in [0..80]]) )); // G. C. Greubel, Nov 03 2019 (Sage) def A185328_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( 1/product((1-x^(m+8)) for m in (0..80)) ).list() A185328_list(70) # G. C. Greubel, Nov 03 2019 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), this sequence (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), A026796 (g=3), A026797 (g=4), A026798 (g=5), A026799 (g=6), A026800(g=7), A026801 (g=8), A026802 (g=9), A026803 (g=10). Sequence in context: A026826 A025151 A026801 * A210718 A027191 A122522 Adjacent sequences:  A185325 A185326 A185327 * A185329 A185330 A185331 KEYWORD nonn,easy AUTHOR Jason Kimberley, Jan 31 2012 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 15 18:33 EDT 2021. Contains 345049 sequences. (Running on oeis4.)