A263847 - OEIS

%I #16 Oct 10 2018 06:15:23

%S 0,1,3,6,13,24,43,74,124,200,319,496,760,1147,1710,2514,3664,5282,

%T 7548,10696,15044,20999,29128,40140,54995,74927,101556,136950,183832,

%U 245643,326847,433125,571747,751905,985350,1286838,1675080,2173576,2811888,3626974,4665196,5984231,7656041,9769972

%N a(n) = p(2*n)-p(2*n-2)-p(n) where p(n) are the partition numbers A000041(n).

%H Reinhard Zumkeller, <a href="/A263847/b263847.txt">Table of n, a(n) for n = 1..1000</a>

%H S. Mertens, <a href="http://arxiv.org/abs/1502.06635">Small random instances of the stable roommates problem</a>, arXiv preprint arXiv:1502.06635 [math.CO], 2015.

%p with(combinat): seq(numbpart(2*n)-numbpart(2*n-2)-numbpart(n),n=1..45); # _Muniru A Asiru_, Oct 10 2018

%t a[n_] := PartitionsP[2n] - PartitionsP[2n - 2] - PartitionsP[n];

%t Array[a, 44] (* _Jean-François Alcover_, Oct 10 2018 *)

%o (PARI) vector(100, n, numbpart(2*n)-numbpart(2*n-2)-numbpart(n)) \\ _Altug Alkan_, Nov 11 2015

%o (Haskell)

%o a263847 n = a263847_list !! (n-1)

%o a263847_list = 0 : zipWith (-)

%o    (zipWith (-) (tail qs) qs) (drop 2 a000041_list)

%o    where qs = es $ tail a000041_list

%o          es [] = []; es [x] = []; es (_:x:xs) = x : es xs

%o -- _Reinhard Zumkeller_, Nov 12 2015

%o (GAP) List([1..45],n->NrPartitions(2*n)-NrPartitions(2*n-2)-NrPartitions(n)); # _Muniru A Asiru_, Oct 10 2018

%Y Cf. A000041.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Nov 11 2015