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A295205
T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.
7
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 8, 4, 1, 1, 6, 14, 14, 6, 1, 1, 9, 25, 42, 25, 9, 1, 1, 13, 53, 108, 108, 53, 13, 1, 1, 19, 111, 284, 438, 284, 111, 19, 1, 1, 28, 217, 777, 1597, 1597, 777, 217, 28, 1, 1, 41, 426, 2146, 5831, 8241, 5831, 2146, 426, 41, 1, 1, 60, 860, 5887
OFFSET
1,5
COMMENTS
Table starts
.1..1...1....1.....1.......1........1.........1..........1...........1
.1..2...3....4.....6.......9.......13........19.........28..........41
.1..3...8...14....25......53......111.......217........426.........860
.1..4..14...42...108.....284......777......2146.......5887.......16061
.1..6..25..108...438....1597.....5831.....21717......81590......307267
.1..9..53..284..1597....8241....40924....205338....1042704.....5314555
.1.13.111..777..5831...40924...279663...1900344...12981261....89115875
.1.19.217.2146.21717..205338..1900344..17574795..162114347..1498926338
.1.28.426.5887.81590.1042704.12981261.162114347.2023191364.25252046266
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +a(n-3)
k=3: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) +a(n-4) -2*a(n-5)
k=4: [order 13]
k=5: [order 32]
k=6: [order 85]
EXAMPLE
Some solutions for n=6 k=4
..0..1..1..0. .1..1..1..0. .0..1..1..0. .0..1..1..1. .1..1..1..0
..0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..0..1. .1..0..1..1
..0..0..0..0. .1..0..1..0. .0..0..0..0. .0..1..0..1. .1..1..0..1
..0..0..1..1. .1..0..1..0. .0..0..1..1. .1..1..0..1. .0..1..0..1
..0..0..1..1. .1..0..1..0. .0..1..1..1. .1..0..1..1. .0..1..0..1
..0..0..0..0. .1..1..1..0. .0..1..1..0. .1..1..1..0. .0..1..1..1
CROSSREFS
Column 2 is A000930(n+1).
Sequence in context: A347148 A202756 A156354 * A297020 A099597 A358146
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 16 2017
STATUS
approved