A202443 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

338, 574, 1102, 1890, 3122, 4822, 7238, 10394, 14602, 19886, 26622, 34834, 44962, 57030, 71542, 88522, 108538, 131614, 158382, 188866, 223762, 263094, 307622, 357370, 413162, 475022, 543838, 619634, 703362, 795046, 895702, 1005354, 1125082

Offset

1,1

Comments

Column 4 of A202447.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7) for n>8.

Conjectures from Colin Barker, May 29 2018: (Start)

G.f.: 2*x*(169 - 220*x - 141*x^2 + 424*x^3 - 133*x^4 - 176*x^5 + 137*x^6 - 28*x^7) / ((1 - x)^5*(1 + x)^2).

a(n) = (2/3)*(n^4 + 12*n^3 + 59*n^2 + 177*n + 159) for n even.

a(n) = (2/3)*(n^4 + 12*n^3 + 59*n^2 + 183*n + 168) for n>1 and odd.

(End)

Example

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

Crossrefs

Cf. A202447.

Sequence in context: A226539 A066478 A261707 * A188213 A250802 A186052

Adjacent sequences: A202440 A202441 A202442 * A202444 A202445 A202446

Keyword

nonn

Author

R. H. Hardin, Dec 19 2011

Status

approved