OFFSET
1,27
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
G.f.: x^9 * Product_{m>=9} 1/(1-x^m).
a(n+9) = p(n) -p(n-1) -p(n-2) +p(n-5) +p(n-7) +p(n-9) -p(n-11) -2*p(n-12) -p(n-13) -p(n-15) +p(n-16) +p(n-17) +2*p(n-18) +p(n-19) +p(n-20) -p(n-21) -p(n-23) -2*p(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). - 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
G.f.: Sum_{k>=1} x^(9*k) / Product_{j=1..k-1} (1 - x^j). - Ilya Gutkovskiy, Nov 25 2020
MAPLE
seq(coeff(series(x^9/mul(1-x^(m+9), m = 0..85), x, n+1), x, n), n = 1..80); # G. C. Greubel, Nov 03 2019
MATHEMATICA
Table[Count[IntegerPartitions[n], _?(Min[#]==9&)], {n, 80}] (* Harvey P. Dale, May 09 2013 *)
Rest@CoefficientList[Series[x^9/QPochhammer[x^9, x], {x, 0, 80}], x] (* G. C. Greubel, Nov 03 2019 *)
PROG
(PARI) my(x='x+O('x^70)); concat(vector(8), Vec(x^9/prod(m=0, 85, 1-x^(m+9)))) \\ G. C. Greubel, Nov 03 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 80); [0, 0, 0, 0, 0, 0, 0, 0] cat Coefficients(R!( x^9/(&*[1-x^(m+9): m in [0..85]]) )); // G. C. Greubel, Nov 03 2019
(Sage)
def A026802_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^9/product((1-x^(m+9)) for m in (0..85)) ).list()
a=A026802_list(81); a[1:] # 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), 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).
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Arlin Anderson (starship1(AT)gmail.com), Apr 12 2001
STATUS
approved