A183767 1/32 the number of (n+1) X 5 binary arrays with equal numbers of 2 X 2 subblocks with sum mod two being 0 and 1.

12, 280, 7392, 205920, 5912192, 173065984, 5134924800, 153876579840, 4646469273600, 141154845511680, 4309194677698560, 132086184685977600, 4062564621910867968, 125316146802859048960, 3875293808717379141632

Offset: 1

Author

R. H. Hardin, Jan 06 2011

Keywords

• nonn

Examples

			Some solutions for 3 X 5:
..0..0..1..1..0....0..0..0..1..1....1..0..1..1..1....0..0..0..1..1
..0..0..0..0..0....1..1..1..1..1....1..1..0..0..1....0..1..1..1..0
..0..0..0..1..0....0..1..0..0..1....1..1..1..1..1....0..0..0..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Column 4 of A183772.

Formula

Empirically a(n) = 2^(3*n)*Gamma(2*n+1/2)/(Gamma(n+1/2)*n!). - Peter Luschny, Sep 24 2018

Conjectures from Peter Bala, Mar 11 2025: (Start)

1) a(n) = 2^n * binomial(4*n, 2*n).

2) a(n) = (4/3) * [x^n] T(3*n, 1 + x), where T(n, x) denotes the n-th Chebyshev polynomial of the first kind. (End)