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

1,1

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)

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 *)

Crossrefs

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

Sequence in context: A032091 A182994 A309691 * A192706 A248832 A280400

Adjacent sequences: A235789 A235790 A235791 * A235793 A235794 A235795

Keyword

nonn

Author

Omar E. Pol, Jan 18 2014

Extensions

More terms from Alois P. Heinz, Jan 21 2014

Status

approved