A202048 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.

636, 1968, 4980, 11016, 22092, 41088, 71964, 120000, 192060, 296880, 445380, 651000, 930060, 1302144, 1790508, 2422512, 3230076, 4250160, 5525268, 7103976, 9041484, 11400192, 14250300, 17670432, 21748284, 26581296, 32277348, 38955480

Offset

1,1

Comments

Column 4 of A202052.

Links

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

Formula

Empirical: a(n) = (1/30)*n^6 + (9/10)*n^5 + (59/6)*n^4 + (111/2)*n^3 + (2552/15)*n^2 + (1278/5)*n + 144.

Conjectures from Colin Barker, May 25 2018: (Start)

G.f.: 12*x*(53 - 207*x + 380*x^2 - 398*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

(End)

Example

Some solutions for n=3:
..0..1..0..0..0..0....0..0..0..0..0..0....1..0..1..0..1..0....1..0..0..0..0..0
..1..0..0..0..0..0....1..0..1..0..1..1....0..1..0..1..0..0....1..0..1..1..1..1
..0..1..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0
..1..0..0..0..0..0....1..0..1..0..1..1....0..0..0..0..0..0....1..0..1..1..1..1
..0..0..0..0..0..0....1..0..0..0..0..0....1..0..0..0..0..0....1..0..1..1..1..1

Crossrefs

Cf. A202052.

Sequence in context: A250581 A061623 A253506 * A251039 A203054 A198774

Adjacent sequences: A202045 A202046 A202047 * A202049 A202050 A202051

Keyword

nonn

Author

R. H. Hardin, Dec 10 2011

Status

approved