A335357 Number of compositions of n such that every subsequence has a different sum.

1, 1, 1, 3, 3, 5, 5, 13, 13, 27, 21, 41, 41, 61, 55, 111, 105, 185, 155, 313, 259, 495, 387, 701, 623, 961, 805, 1419, 1191, 1781, 1481, 2437, 2161, 3387, 2745, 4457, 3965, 5821, 4867, 8223, 6909, 10625, 8591, 14617, 11887, 18735, 14991, 24821, 20291, 32113

Offset: 0

Author

Alois P. Heinz, Jun 03 2020

Keywords

• nonn

Comments

All terms are odd.

Examples

			a(7) = 13: 7, 16, 25, 34, 43, 52, 61, 124, 142, 214, 241, 412, 421.
a(8) = 13: 8, 17, 26, 35, 53, 62, 71, 125, 152, 215, 251, 512, 521.
a(9) = 27: 9, 18, 27, 36, 45, 54, 63, 72, 81, 126, 135, 153, 162, 216, 234, 243, 261, 315, 324, 342, 351, 423, 432, 513, 531, 612, 621.
a(10) = 21: 10, 19, 28, 37, 46, 64, 73, 82, 91, 127, 136, 163, 172, 217, 271, 316, 361, 613, 631, 712, 721.
		

Links

• Fausto A. C. Cariboni, Table of n, a(n) for n = 0..700 (terms 0..100 from Alois P. Heinz)

Crossrefs

Cf. A032020, A275972 (the same for partitions).

Programs

Maple

b:= proc(n, s) option remember; `if`(n=0, 1, add((h-> `if`(nops(s)*
      2=nops(h), b(n-j, h), 0))({s[], map(x-> x+j, s)[]}), j=1..n))
    end:
a:= n-> b(n, {0}):
seq(a(n), n=0..40);

Mathematica

b[n_, s_] := b[n, s] = If[n == 0, 1, Sum[Function[h, If[Length[s]*
     2 == Length[h], b[n - j, h], 0]][Union@Join[s, s + j]], {j, 1, n}]];
a[n_] := b[n, {0}];
Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 13 2022, after Alois P. Heinz *)