A367680 Number of integer compositions x1+x2+...+xk of n such that each xj has exactly j bits set.

1, 1, 1, 0, 2, 1, 1, 3, 2, 1, 2, 4, 2, 4, 6, 2, 4, 5, 10, 7, 10, 12, 8, 6, 11, 14, 16, 13, 16, 16, 14, 14, 30, 32, 19, 35, 28, 23, 27, 38, 36, 47, 44, 42, 55, 52, 51, 85, 88, 74, 84, 84, 72, 81, 102, 110, 122, 115, 108, 132, 137, 136, 179, 195, 164, 160, 181

Offset: 0

Author

Arnauld Chevallier, Nov 26 2023

Keywords

• nonn
• base

Examples

			There are 6 such compositions for n = 14:
  14 = 1 + 6 + 7 (1 + 110 + 111)
  14 = 2 + 5 + 7 (10 + 101 + 111)
  14 = 2 + 12 (10 + 1100)
  14 = 4 + 3 + 7 (100 + 11 + 111)
  14 = 4 + 10 (100 + 1010)
  14 = 8 + 6 (1000 + 110)
Therefore a(14) = 6.
		

Crossrefs

Cf. A000079, A000120, A018900, A014311, A014313, A023688, A023689, A023690, A023691.

Programs

PARI

a(n) = my(nb=0); forpart(v=n, if (vecsort(apply(hammingweight, Vec(v))) == [1..#v], nb++)); nb; \\ Michel Marcus, Nov 28 2023