A336902 Sum of the smallest parts of all compositions of n into distinct parts.

0, 1, 2, 5, 6, 11, 18, 25, 32, 53, 84, 107, 156, 205, 302, 497, 618, 863, 1206, 1597, 2228, 3569, 4440, 6191, 8256, 11329, 14642, 20477, 30390, 38555, 52578, 69625, 92696, 122141, 160500, 211955, 310476, 386941, 521102, 678617, 901386, 1155383, 1529742, 1940749

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) = 18 = 1 + 1 + 1 + 1 + 1 + 1 + 2 + 2 + 1 + 1 + 6: (1)23, (1)32, 2(1)3, 23(1), 3(1)2, 32(1), (2)4, 4(2), (1)5, 5(1), (6).

Maple

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

Mathematica

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

Crossrefs

Cf. A005895, A006128, A046746, A092265, A097939, A102712, A336903.

Sequence in context: A088273 A049054 A319140 * A135476 A255310 A051217

Adjacent sequences: A336899 A336900 A336901 * A336903 A336904 A336905

Keyword

nonn

Author

Alois P. Heinz, Aug 07 2020

Status

approved