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

0,2

Comments

For the definition of overcomposition see A236002.

The equivalent sequence for overpartitions is A235792.

Row sums of triangle A236628.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A107762 A253901 A027562 * A096259 A338614 A087645

Adjacent sequences: A236622 A236623 A236624 * A236626 A236627 A236628

Keyword

nonn

Author

Omar E. Pol, Feb 01 2014

Extensions

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

Status

approved