login
A263847
a(n) = p(2*n)-p(2*n-2)-p(n) where p(n) are the partition numbers A000041(n).
1
0, 1, 3, 6, 13, 24, 43, 74, 124, 200, 319, 496, 760, 1147, 1710, 2514, 3664, 5282, 7548, 10696, 15044, 20999, 29128, 40140, 54995, 74927, 101556, 136950, 183832, 245643, 326847, 433125, 571747, 751905, 985350, 1286838, 1675080, 2173576, 2811888, 3626974, 4665196, 5984231, 7656041, 9769972
OFFSET
1,3
LINKS
S. Mertens, Small random instances of the stable roommates problem, arXiv preprint arXiv:1502.06635 [math.CO], 2015.
MAPLE
with(combinat): seq(numbpart(2*n)-numbpart(2*n-2)-numbpart(n), n=1..45); # Muniru A Asiru, Oct 10 2018
MATHEMATICA
a[n_] := PartitionsP[2n] - PartitionsP[2n - 2] - PartitionsP[n];
Array[a, 44] (* Jean-François Alcover, Oct 10 2018 *)
PROG
(PARI) vector(100, n, numbpart(2*n)-numbpart(2*n-2)-numbpart(n)) \\ Altug Alkan, Nov 11 2015
(Haskell)
a263847 n = a263847_list !! (n-1)
a263847_list = 0 : zipWith (-)
(zipWith (-) (tail qs) qs) (drop 2 a000041_list)
where qs = es $ tail a000041_list
es [] = []; es [x] = []; es (_:x:xs) = x : es xs
-- Reinhard Zumkeller, Nov 12 2015
(GAP) List([1..45], n->NrPartitions(2*n)-NrPartitions(2*n-2)-NrPartitions(n)); # Muniru A Asiru, Oct 10 2018
CROSSREFS
Cf. A000041.
Sequence in context: A128517 A022568 A120006 * A061567 A293076 A293421
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 11 2015
STATUS
approved