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A297544
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 3 neighboring 1s.
13
1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 35, 7, 1, 1, 38, 93, 88, 14, 1, 1, 105, 197, 275, 461, 31, 1, 1, 381, 905, 1233, 2205, 2050, 69, 1, 1, 1067, 4617, 10234, 12161, 13248, 8057, 155, 1, 1, 2676, 17190, 65363, 205888, 94647, 67215, 35640, 354, 1, 1, 7533, 60751, 355573
OFFSET
1,5
COMMENTS
Table starts
.1...1......1.......1........1...........1.............1..............1
.1...2.....11......24.......38.........105...........381...........1067
.1...4.....35......93......197.........905..........4617..........17190
.1...7.....88.....275.....1233.......10234.........65363.........355573
.1..14....461....2205....12161......205888.......2748026.......25141813
.1..31...2050...13248....94647.....3015179......67372651......916902295
.1..69...8057...67215...754342....45293985....1610981344....33425081735
.1.155..35640..401415..6315609...726450667...45496070039..1479214192234
.1.354.158090.2403621.51451261.11267743659.1204223924807.59920115456355
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5)
k=3: [order 14]
k=4: [order 22]
k=5: [order 54]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6)
n=3: [order 17]
n=4: [order 40]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..0. .1..1..0..0. .0..0..1..0. .0..0..1..0
..1..1..1..0. .0..1..1..1. .0..1..1..1. .0..1..1..1. .1..1..1..1
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..0..0
..0..0..1..1. .1..1..1..0. .0..0..1..1. .0..1..1..0. .0..0..1..1
..0..0..1..1. .0..1..0..0. .0..1..1..1. .0..1..1..1. .0..0..1..1
CROSSREFS
Column 2 is A202973.
Sequence in context: A372960 A110905 A205447 * A297802 A232266 A234013
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 31 2017
STATUS
approved