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A317815
T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
8
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 5, 4, 4, 5, 1, 1, 10, 5, 7, 5, 10, 1, 1, 23, 8, 34, 34, 8, 23, 1, 1, 54, 9, 56, 38, 56, 9, 54, 1, 1, 131, 28, 77, 94, 94, 77, 28, 131, 1, 1, 321, 44, 228, 230, 142, 230, 228, 44, 321, 1, 1, 789, 60, 551, 552, 434, 434, 552, 551, 60, 789, 1
OFFSET
1,5
COMMENTS
Table starts
.1...1..1...1....1....1.....1.....1......1......1.......1.......1........1
.1...2..2...3....5...10....23....54....131....321.....789....1943.....4788
.1...2..2...4....5....8.....9....28.....44.....60.....118.....256......409
.1...3..4...7...34...56....77...228....551...1300....3171....6929....16038
.1...5..5..34...38...94...230...552...1397...3674....9184...23878....60774
.1..10..8..56...94..142...434..1071...2279...6087...15953...40210...104488
.1..23..9..77..230..434..1575..4232..10738..32307...97258..284543...844473
.1..54.28.228..552.1071..4232.13712..35752.110093..343180.1067786..3331483
.1.131.44.551.1397.2279.10738.35752.112854.377515.1253484.4165180.14146154
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4) -a(n-5) -a(n-6)
k=3: [order 17] for n>19
k=4: [order 48] for n>52
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..0. .0..1..1..1. .0..1..0..1. .0..1..1..1
..0..0..0..0. .1..0..0..1. .1..0..0..0. .1..0..0..0. .1..0..0..0
..0..0..0..0. .0..0..1..0. .0..0..0..1. .1..0..1..1. .0..0..1..1
..0..0..0..0. .1..1..1..0. .1..1..1..0. .0..1..1..0. .1..1..1..0
..0..0..0..0. .0..1..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1
CROSSREFS
Sequence in context: A326038 A122632 A176809 * A318423 A318091 A301608
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 07 2018
STATUS
approved