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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.
14
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 24 2016
STATUS
approved