OFFSET
0,3
COMMENTS
a(n+1) is the number of partitions p of 2n-1 such that (number of parts of p) is a part of p, for n >=0. - Clark Kimberling, Mar 02 2014
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Marco Baggio, Vasilis Niarchos, Kyriakos Papadodimas, and Gideon Vos, Large-N correlation functions in N = 2 superconformal QCD, arXiv preprint arXiv:1610.07612 [hep-th], 2016.
K. Blum, Bounds on the Number of Graphical Partitions, arXiv:2103.03196 [math.CO], 2021. See Table on p. 7.
FORMULA
a(n) = p(2*n) - p(2*n-1), where p is the partition function, A000041. - George Beck, Jun 05 2017 [Shifted by Georg Fischer, Jun 20 2022]
MAPLE
b:= proc(n, i) option remember;
if n<0 then 0
elif n=0 then 1
elif i<2 then 0
else b(n, i-1) +b(n-i, i)
fi
end:
a:= n-> b(2*n, 2*n):
seq(a(n), n=0..40); # Alois P. Heinz, Dec 01 2010
MATHEMATICA
Table[Count[IntegerPartitions[2 n -1], p_ /; MemberQ[p, Length[p]]], {n, 20}] (* Clark Kimberling, Mar 02 2014 *)
b[n_, i_] := b[n, i] = Which[n<0, 0, n==0, 1, i<2, 0, True, b[n, i-1] + b[n-i, i]]; a[n_] := b[2*n, 2*n]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Sep 21 2015, after Alois P. Heinz *)
a[n_] := PartitionsP[2*n] - PartitionsP[2*n - 1]; Table[a[n], {n, 0, 40}] (* George Beck, Jun 05 2017 *)
PROG
(PARI) a(n)=numbpart(2*n)-numbpart(2*n-1) \\ Charles R Greathouse IV, Jun 06 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Dec 01 2010
EXTENSIONS
More terms from Alois P. Heinz, Dec 01 2010
STATUS
approved