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

2,2

Links

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

Formula

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

Example

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}.

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);

Crossrefs

Column k=2 of A292506.

Cf. A027306, A292549.

Sequence in context: A080204 A115982 A167243 * A185828 A134438 A092255

Adjacent sequences: A316400 A316401 A316402 * A316404 A316405 A316406

Keyword

nonn

Author

Alois P. Heinz, Jul 02 2018

Status

approved