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

0,4

Comments

All terms are odd.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A289768 A161220 A032022 * A325679 A147198 A147048

Adjacent sequences: A335354 A335355 A335356 * A335358 A335359 A335360

Keyword

nonn

Author

Alois P. Heinz, Jun 03 2020

Status

approved