A336903 Sum of the largest parts of all compositions of n into distinct parts.

0, 1, 2, 7, 10, 19, 42, 61, 98, 151, 304, 403, 654, 925, 1400, 2431, 3328, 4903, 7056, 10117, 13952, 23419, 30406, 44683, 61308, 87289, 116822, 164359, 247774, 327715, 457542, 624445, 855062, 1148023, 1559188, 2058643, 3043506, 3906637, 5375732, 7111975, 9679852

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Formula

a(n) == n (mod 2).

Example

a(6) = 42 = 3 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 5 + 5 + 6: 12(3), 1(3)2, 21(3), 2(3)1, (3)12, (3)21, 2(4), (4)2, 1(5), (5)1, (6).

Maple

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, p!, b(n-i, min(n-i, i-1), p+1)*
      `if`(p=0, i, 1)+b(n, i-1, p)))
    end:
a:= n-> `if`(n=0, 0, b(n$2, 0)):
seq(a(n), n=0..50);

Mathematica

b[n_, i_, p_] := b[n, i, p] = If[i(i + 1)/2 < n, 0,
     If[n == 0, p!, b[n - i, Min[n - i, i - 1], p + 1]*
     If[p == 0, i, 1] + b[n, i - 1, p]]];
a[n_] := If[n == 0, 0, b[n, n, 0]];
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 12 2021, after Alois P. Heinz *)

Crossrefs

Cf. A005895, A006128, A046746, A092265, A097939, A102712, A336902.

Sequence in context: A309805 A125852 A368824 * A155171 A049830 A270879

Adjacent sequences: A336900 A336901 A336902 * A336904 A336905 A336906

Keyword

nonn

Author

Alois P. Heinz, Aug 07 2020

Status

approved