A319776 Number of partitions of 2n in which any two distinct parts differ by at least n.

1, 2, 4, 6, 8, 9, 14, 13, 17, 20, 23, 22, 31, 28, 33, 38, 40, 39, 49, 45, 54, 57, 58, 57, 70, 68, 71, 76, 81, 78, 93, 86, 94, 98, 99, 104, 116, 109, 114, 119, 128, 123, 138, 131, 140, 149, 146, 145, 162, 158, 166, 168, 173, 170, 185, 184, 193, 194, 195, 194

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..2000 from Alois P. Heinz)

Formula

a(n) = A218698(2n,n).

Maple

g:= proc(n, i) option remember;
      add(`if`(irem(n, j)=0, 1, 0), j=1..i)
    end:
a:= proc(n) option remember; numtheory[tau](2*n)+
      add(g(2*n-j, min(2*n-j, j-n)), j=n+1..2*n-1)
    end: a(0):=1:
seq(a(n), n=0..100);

Mathematica

g[n_, i_] := g[n, i] = Sum[If[Mod[n, j] == 0, 1, 0], {j, 1, i}];
a[n_] := a[n] = DivisorSigma[0, 2n] + Sum[g[2n - j, Min[2n - j, j - n]], {j, n + 1, 2n - 1}]; a[0] = 1;
a /@ Range[0, 100] (* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)

Crossrefs

Cf. A218698.

Sequence in context: A074901 A189294 A125990 * A191921 A227979 A349151

Adjacent sequences: A319773 A319774 A319775 * A319777 A319778 A319779

Keyword

nonn

Author

Alois P. Heinz, Sep 27 2018

Status

approved