A235792 Total number of parts in all overpartitions of n.

2, 6, 16, 34, 68, 128, 228, 390, 650, 1052, 1664, 2584, 3940, 5916, 8768, 12826, 18552, 26566, 37672, 52956, 73848, 102192, 140420, 191688, 260038, 350700, 470384, 627604, 833236, 1101080, 1448500, 1897438, 2475464, 3217016, 4165200, 5373714, 6909180, 8854288

Offset: 1

Author

Omar E. Pol, Jan 18 2014

Keywords

• nonn

Comments

It appears that a(n) is also the sum of largest parts of all overpartitions of n.

More generally, It appears that the total number of parts >= k in all overpartitions of n equals the sum of k-th largest parts of all overpartitions of n. In this case k = 1. Also the first column of A235797.

The equivalent sequence for partitions is A006128.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)

Crossrefs

Cf. A006128, A015128, A211971, A235790, A235793, A235797, A235798, A236000, A236001.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(i<1, [0$2], b(n, i-1)+add((l-> l+[0, l[1]*j])
       (2*b(n-i*j, i-1)), j=1..n/i)))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..40);  # Alois P. Heinz, Jan 21 2014

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Sum[ Function[l, l+{0, l[[1]]*j}][2*b[n-i*j, i-1]], {j, 1, n/i}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Nov 11 2015, after Alois P. Heinz *)

Formula

log(a(n)) ~ Pi*sqrt(n). - Vaclav Kotesovec, Apr 13 2025

Extensions

More terms from Alois P. Heinz, Jan 21 2014