A292548 Number of multisets of nonempty binary words with a total of n letters such that no word has a majority of 0's.

1, 1, 4, 8, 25, 53, 148, 328, 858, 1938, 4862, 11066, 27042, 61662, 147774, 336854, 795678, 1810466, 4228330, 9597694, 22211897, 50279985, 115489274, 260686018, 594986149, 1339215285, 3040004744, 6823594396, 15416270130, 34510814918, 77644149076, 173368564396

Offset: 0

Author

Alois P. Heinz, Sep 18 2017

Keywords

• nonn

Examples

			a(0) = 1: {}.
a(1) = 1: {1}.
a(2) = 4: {01}, {10}, {11}, {1,1}.
a(3) = 8: {011}, {101}, {110}, {111}, {1,01}, {1,10}, {1,11}, {1,1,1}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3213

Crossrefs

Row sums of A292506.

Column k=2 of A292712.

Cf. A027306.

Programs

Maple

g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
      g(d), d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..35);

Mathematica

g[n_] :=  2^(n-1) + If[OddQ[n], 0, Binomial[n, n/2]/2];
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*
     g[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Apr 30 2022, after Alois P. Heinz *)

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^A027306(j).

Euler transform of A027306.