A367680 - OEIS

%I #23 Nov 28 2023 09:14:44

%S 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,

%T 14,14,30,32,19,35,28,23,27,38,36,47,44,42,55,52,51,85,88,74,84,84,72,

%U 81,102,110,122,115,108,132,137,136,179,195,164,160,181

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

%e There are 6 such compositions for n = 14:

%e   14 = 1 + 6 + 7 (1 + 110 + 111)

%e   14 = 2 + 5 + 7 (10 + 101 + 111)

%e   14 = 2 + 12 (10 + 1100)

%e   14 = 4 + 3 + 7 (100 + 11 + 111)

%e   14 = 4 + 10 (100 + 1010)

%e   14 = 8 + 6 (1000 + 110)

%e Therefore a(14) = 6.

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

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

%K nonn,base

%O 0,5

%A _Arnauld Chevallier_, Nov 26 2023