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

Author

Alois P. Heinz, Sep 27 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A218698.

Programs

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 *)

Formula

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