A207109 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

18, 324, 1504, 4534, 10898, 22714, 42874, 75198, 124602, 197280, 300900, 444814, 640282, 900710, 1241902, 1682326, 2243394, 2949756, 3829608, 4915014, 6242242, 7852114, 9790370, 12108046, 14861866, 18114648, 21935724, 26401374, 31595274

Offset

1,1

Comments

Column 6 of A207111.

Links

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

Formula

Empirical: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6.

Conjectures from Colin Barker, Jun 19 2018: (Start)

G.f.: 2*x*(9 + 99*x - 193*x^2 + 90*x^3 + 17*x^4 - 18*x^5 + 3*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

Some solutions for n=4:
..0..0..1..0..1..0....1..1..1..1..1..0....1..1..0..0..1..0....0..1..0..1..0..0
..0..1..0..1..0..1....0..0..1..0..0..1....1..0..1..0..0..1....1..0..1..0..1..0
..0..1..0..0..1..0....0..0..1..0..1..0....1..1..1..0..0..1....1..1..0..0..1..0
..0..1..0..0..1..0....0..0..1..0..1..0....1..1..1..0..0..1....1..1..1..0..1..0

Crossrefs

Cf. A207111.

Sequence in context: A207022 A207366 A187381 * A207465 A207240 A207498

Adjacent sequences: A207106 A207107 A207108 * A207110 A207111 A207112

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved