A188841 Number of n X 7 binary arrays without the pattern 0 1 diagonally or vertically.

128, 987, 3280, 7753, 15504, 28101, 47652, 76912, 119416, 179630, 263120, 376740, 528840, 729495, 990756, 1326924, 1754848, 2294248, 2968064, 3802832, 4829088, 6081801, 7600836, 9431448, 11624808, 14238562, 17337424, 20993804, 25288472

Offset

1,1

Comments

Column 7 of A188843.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = (1/5040)*n^7 + (1/72)*n^6 + (143/360)*n^5 + (53/9)*n^4 + (33667/720)*n^3 + (12679/72)*n^2 + (9439/70)*n - 572 for n>4.

Empirical g.f.: x*(128 - 37*x - 1032*x^2 + 1981*x^3 - 992*x^4 - 605*x^5 + 700*x^6 - 58*x^7 - 96*x^8 + 3*x^9 + 8*x^10 + x^11) / (1 - x)^8. - Colin Barker, May 01 2018

Example

Some solutions for 3 X 7:
..1..1..0..0..1..1..1....1..1..1..1..1..1..1....1..0..0..1..1..0..0
..1..1..0..0..0..1..1....1..1..0..1..1..1..1....1..0..0..0..1..0..0
..1..1..0..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0

Crossrefs

Cf. A188843.

Sequence in context: A372094 A297643 A224043 * A188704 A297344 A183976

Adjacent sequences: A188838 A188839 A188840 * A188842 A188843 A188844

Keyword

nonn

Author

R. H. Hardin, Apr 12 2011

Status

approved