A279977 T(n,k) is the number of n X k 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.

0, 1, 0, 0, 3, 0, 3, 9, 9, 0, 3, 24, 50, 31, 0, 9, 62, 221, 296, 108, 0, 15, 134, 822, 1922, 1650, 366, 0, 31, 277, 2669, 10491, 15511, 8666, 1205, 0, 57, 542, 8068, 50690, 124030, 118857, 43543, 3873, 0, 108, 1035, 23169, 226771, 887491, 1393359, 876704, 211650

Offset

1,5

Links

R. H. Hardin, Table of n, a(n) for n = 1..198

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 9*a(n-1) -30*a(n-2) +45*a(n-3) -30*a(n-4) +9*a(n-5) -a(n-6)

k=3: [order 9] for n>10

k=4: [order 24]

k=5: [order 38] for n>39

k=6: [order 96] for n>97

Empirical for row n:

n=1: a(n) = 3*a(n-1) -5*a(n-3) +3*a(n-5) +a(n-6)

n=2: [order 8] for n>10

n=3: [order 24] for n>30

n=4: [order 68] for n>78

Example

Table starts:
.0.....1.......0.........3...........3............9.............15
.0.....3.......9........24..........62..........134............277
.0.....9......50.......221.........822.........2669...........8068
.0....31.....296......1922.......10491........50690.........226771
.0...108....1650.....15511......124030.......887491........5870751
.0...366....8666....118857.....1393359.....14787217......144819856
.0..1205...43543....876704....15071233....237386464.....3444870482
.0..3873..211650...6281773...158391708...3703836674....79672440007
.0.12207.1002602..43997218..1627160233..56499013470..1801951754910
.0.37859.4652327.302544617.16409869901.846166990079.40020022178950
...
Some solutions for n=4 and k=4:
..0..1..0..0. .0..1..0..0. .0..1..0..1. .0..0..1..0. .0..1..0..1
..0..0..1..0. .0..1..1..0. .0..1..0..0. .1..0..1..0. .1..0..1..1
..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1. .1..0..1..1
..1..0..0..1. .0..0..1..0. .0..0..0..1. .1..0..0..1. .0..1..0..1

Crossrefs

Row 1 is A105423(n-2).

Sequence in context: A021333 A348670 A104141 * A060533 A177785 A212036

Adjacent sequences: A279974 A279975 A279976 * A279978 A279979 A279980

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 24 2016

Status

approved