A202093 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 011 in rows and columns.

108, 324, 720, 1600, 3000, 5625, 9450, 15876, 24696, 38416, 56448, 82944, 116640, 164025, 222750, 302500, 399300, 527076, 679536, 876096, 1107288, 1399489, 1739010, 2160900, 2646000, 3240000, 3916800, 4734976, 5659776, 6765201, 8005878

Offset: 1

Author

R. H. Hardin, Dec 11 2011

Keywords

• nonn

Comments

Column 1 of A202100.

Examples

			Some solutions for n=10:
..1..1..1....1..1..0....1..1..1....1..1..1....1..1..1....1..0..0....1..0..0
..1..1..0....1..1..0....1..1..1....1..1..0....0..0..0....1..1..0....1..1..1
..0..1..0....1..0..0....1..1..1....1..0..0....1..0..1....1..0..0....1..0..0
..1..1..0....1..1..0....1..1..1....1..1..0....0..0..0....1..1..0....1..1..1
..0..0..0....1..0..0....1..0..1....0..0..0....1..0..1....1..0..0....1..0..0
..1..1..0....1..1..0....1..1..1....1..1..0....0..0..0....0..1..0....1..1..1
..0..0..0....1..0..0....1..0..1....0..0..0....1..0..0....1..0..0....1..0..0
..0..1..0....1..1..0....1..0..1....1..1..0....0..0..0....0..1..0....1..1..1
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....1..0..0....1..0..0
..0..1..0....1..0..0....0..0..0....0..0..0....0..0..0....0..1..0....1..1..1
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....1..0..0....1..0..0
..0..0..0....1..0..0....0..0..0....0..0..0....0..0..0....0..1..0....0..1..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) +4*a(n-2) -10*a(n-3) -5*a(n-4) +20*a(n-5) -20*a(n-7) +5*a(n-8) +10*a(n-9) -4*a(n-10) -2*a(n-11) +a(n-12).

Conjectures from Colin Barker, Feb 20 2018: (Start)

G.f.: x*(108 + 108*x - 360*x^2 - 56*x^3 + 700*x^4 - 115*x^5 - 680*x^6 + 236*x^7 + 334*x^8 - 155*x^9 - 66*x^10 + 36*x^11) / ((1 - x)^7*(1 + x)^5).

a(n) = (n^6 + 28*n^5 + 324*n^4 + 1984*n^3 + 6784*n^2 + 12288*n + 9216) / 256 for n even.

a(n) = (n^6 + 28*n^5 + 321*n^4 + 1928*n^3 + 6395*n^2 + 11100*n + 7875) / 256 for n odd.

(End)