A183776 Half the number of (n+1) X 4 binary arrays with no 2 X 2 subblock having exactly 2 ones.

8, 33, 161, 730, 3435, 15887, 74148, 344483, 1604473, 7462786, 34738575, 161631659, 752241404, 3500410439, 16290047469, 75805472562, 352771994195, 1641641366551, 7639557462868, 35551227927131, 165441007206577, 769893052530306, 3582766049751239, 16672702423031411, 77587874702105452

Offset

0,1

Links

R. H. Hardin, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (2,18,-13,-70,24,64).

Formula

Empirical: a(n) = 2*a(n-1) + 18*a(n-2) - 13*a(n-3) - 70*a(n-4) + 24*a(n-5) + 64*a(n-6).

Empirical g.f.: (8 + 17*x - 49*x^2 - 82*x^3 + 66*x^4 + 88*x^5) / ((1 + 2*x)*(1 - 4*x - 10*x^2 + 33*x^3 + 4*x^4 - 32*x^5)). - Colin Barker, Apr 04 2018

The above g.f. is correct. See A183782 for bounds on the order of the recurrence. - Andrew Howroyd, Jan 09 2025

Example

Some solutions with a(1,1)=0 for 3 X 4:
..0..1..1..1....0..0..0..0....0..0..0..0....0..0..0..0....0..1..0..1
..0..0..1..0....0..0..0..0....0..1..0..1....0..0..1..0....0..0..0..0
..0..0..0..0....0..1..0..0....0..0..0..0....1..0..0..0....1..0..1..0

Crossrefs

Column k=3 of A183782.

Sequence in context: A297683 A346819 A220590 * A001407 A005398 A240044

Adjacent sequences: A183773 A183774 A183775 * A183777 A183778 A183779

Keyword

nonn,easy

Author

R. H. Hardin, Jan 07 2011

Extensions

a(0) prepended by Andrew Howroyd, Jan 09 2025

Status

approved