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A336902
Sum of the smallest parts of all compositions of n into distinct parts.
8
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
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 *)
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 07 2020
STATUS
approved