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

0,5

Links

Table of n, a(n) for n=0..66.

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A243611 A273102 A273104 * A152538 A345033 A329359

Adjacent sequences: A367677 A367678 A367679 * A367681 A367682 A367683

Keyword

nonn,base

Author

Arnauld Chevallier, Nov 26 2023

Status

approved