A202200 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.

1728, 7680, 26400, 76032, 192192, 439296, 926640, 1830400, 3422848, 6110208, 10480704, 17364480, 27907200, 43659264, 66682704, 99677952, 146132800, 210496000, 298378080, 416782080, 574367040, 781747200, 1051830000, 1400196096

Offset

1,1

Comments

Column 6 of A202202.

Links

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

Formula

Empirical: a(n) = (n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/315.

Conjectures from Colin Barker, May 27 2018: (Start)

G.f.: 16*x*(108 - 492*x + 1218*x^2 - 1890*x^3 + 1932*x^4 - 1308*x^5 + 567*x^6 - 143*x^7 + 16*x^8) / (1 - x)^9.

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.

(End)

Example

Some solutions for n=2:
..1..1..1..1..1..1..1..0....0..1..1..1..1..1..1..1....0..1..1..1..0..0..0..0
..1..1..1..1..1..0..0..0....1..1..1..1..1..1..0..0....1..0..0..0..0..0..0..0
..1..1..1..1..0..0..0..0....0..1..1..1..1..0..0..0....1..0..0..0..0..0..0..0
..0..1..1..0..0..0..0..0....0..1..1..1..0..0..0..0....0..0..0..0..0..0..0..0

Crossrefs

Cf. A202202.

Sequence in context: A305475 A202458 A179694 * A251188 A323560 A223236

Adjacent sequences: A202197 A202198 A202199 * A202201 A202202 A202203

Keyword

nonn

Author

R. H. Hardin, Dec 14 2011

Status

approved