A316403 Number of multisets of exactly two nonempty binary words with a total of n letters such that no word has a majority of 0's.

1, 3, 10, 23, 59, 134, 320, 699, 1599, 3434, 7682, 16246, 35762, 74892, 163032, 338771, 731051, 1510466, 3237206, 6658530, 14189790, 29083988, 61687496, 126076638, 266332390, 543061284, 1143207236, 2326521164, 4882706596, 9920514328, 20764519984, 42130081155

Offset: 2

Author

Alois P. Heinz, Jul 02 2018

Keywords

• nonn

Examples

			a(4) = 10: {1,011}, {1,101}, {1,110}, {1,111}, {01,01}, {01,10}, {01,11}, {10,10}, {10,11}, {11,11}.
a(5) = 23: {1,0011}, {1,0101}, {1,0110}, {1,0111}, {1,1001}, {1,1010}, {1,1011}, {1,1100}, {1,1101}, {1,1110}, {1,1111}, {01,011}, {01,101}, {01,110}, {01,111}, {10,011}, {10,101}, {10,110}, {10,111}, {11,011}, {11,101}, {11,110}, {11,111}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..1000

Crossrefs

Column k=2 of A292506.

Cf. A027306, A292549.

Programs

Maple

g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
       binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 3)
    end:
a:= n-> coeff(b(n$2), x, 2):
seq(a(n), n=2..33);

Formula

a(n) = [x^n y^2] 1/Product_{j>=1} (1-y*x^j)^A027306(j).