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

1,1

Comments

Column 1 of A202100.

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)

Example

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

Crossrefs

Sequence in context: A202100 A202492 A369420 * A202485 A202317 A202310

Adjacent sequences: A202090 A202091 A202092 * A202094 A202095 A202096

Keyword

nonn

Author

R. H. Hardin, Dec 11 2011

Status

approved