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

0,3

Links

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

Formula

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

Euler transform of A027306.

Example

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}.

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 *)

Crossrefs

Row sums of A292506.

Column k=2 of A292712.

Cf. A027306.

Sequence in context: A371190 A185615 A068367 * A000964 A297458 A328038

Adjacent sequences: A292545 A292546 A292547 * A292549 A292550 A292551

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2017

Status

approved