A213414 Half the number of n X 4 binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.

8, 128, 1970, 28952, 407498, 5524088, 72544970, 927723512, 11603925098, 142479782648, 1722547903370, 20555827214072, 242622085341098, 2837195512777208, 32916845643156170, 379333828694256632

Offset

1,1

Comments

Column 4 of A213418.

Links

R. H. Hardin, Table of n, a(n) for n = 1..120

Formula

Empirical: a(n) = 51*a(n-1) - 1075*a(n-2) + 11985*a(n-3) - 74524*a(n-4) + 245004*a(n-5) - 332640*a(n-6).

Empirical: a(n) = (5*6^n - 26*7^n + 45*8^n - 14*9^n - 33*10^n + 24*11^n)/2.

Empirical g.f.: 2*x*(4 - 140*x + 2021*x^2 - 14899*x^3 + 55404*x^4 - 83160*x^5) / ((1 - 6*x)*(1 - 7*x)*(1 - 8*x)*(1 - 9*x)*(1 - 10*x)*(1 - 11*x)). - Colin Barker, Jul 21 2018

Example

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

Crossrefs

Cf. A213418.

Sequence in context: A317521 A299650 A300204 * A303417 A303423 A301403

Adjacent sequences: A213411 A213412 A213413 * A213415 A213416 A213417

Keyword

nonn

Author

R. H. Hardin and N. J. A. Sloane, Jun 10 2012

Status

approved