A236625 Total number of parts in all overcompositions of n.

0, 2, 6, 24, 66, 180, 496, 1272, 3202, 7798, 18980, 45076, 106288, 246956, 568776, 1299184, 2944654, 6630660, 14838606, 33026000, 73126376, 161198136, 353812612, 773645124, 1685548792, 3660364490, 7924414752, 17107225340, 36832846344, 79107019964, 169505684844

Offset: 0

Author

Omar E. Pol, Feb 01 2014

Keywords

• nonn

Comments

For the definition of overcomposition see A236002.

The equivalent sequence for overpartitions is A235792.

Row sums of triangle A236628.

Examples

			For n = 3 the 12 overcompositions of 3 are [3], [3'], [1, 2], [1', 2], [1, 2'], [1', 2'], [2, 1], [2', 1], [2, 1'], [2', 1'], [1, 1, 1], [1', 1, 1]. There are 24 parts, so a(3) = 24.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001792, A006128, A235999, A236002, A235792, A236626, A236628, A236633.

Programs

Maple

b:= proc(n, i, p) option remember; `if`(n=0, [p!, 0],
      `if`(i<1, 0, add((p-> p+[0, p[1]*j])(1/j!*
      `if`(j>0, 2, 1)*b(n-i*j, i-1, p+j)), j=0..n/i)))
    end:
a:= n-> b(n$2, 0)[2]:
seq(a(n), n=0..35);  # Alois P. Heinz, Apr 28 2016

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[n == 0, {p!, 0}, If[i < 1, {0, 0}, Sum[# + {0, #[[1]]*j}&[1/j!*If[j > 0, 2, 1]*b[n - i*j, i - 1, p + j]], {j, 0, n/i}]]];
a[n_] := b[n, n, 0][[2]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Nov 03 2022, after Alois P. Heinz *)

Extensions

a(6)-a(30) from Alois P. Heinz, Feb 02 2014