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A297431
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.
13
1, 1, 1, 1, 2, 1, 1, 7, 3, 1, 1, 12, 14, 4, 1, 1, 18, 26, 22, 6, 1, 1, 33, 43, 42, 68, 9, 1, 1, 73, 109, 105, 183, 163, 13, 1, 1, 139, 301, 349, 535, 513, 320, 19, 1, 1, 244, 649, 1057, 2430, 1673, 1085, 782, 28, 1, 1, 449, 1332, 2834, 12005, 11345, 5108, 3332, 1889, 41, 1, 1
OFFSET
1,5
COMMENTS
Table starts
.1..1....1....1.....1.......1........1.........1..........1...........1
.1..2....7...12....18......33.......73.......139........244.........449
.1..3...14...26....43.....109......301.......649.......1332........3124
.1..4...22...42...105.....349.....1057......2834.......8216.......24556
.1..6...68..183...535....2430....12005.....45977.....182298......793315
.1..9..163..513..1673...11345....76692....369339....1884628....11192445
.1.13..320.1085..5108...50127...431723...2741816...19713343...158831909
.1.19..782.3332.19690..267505..3338387..28588498..275287217..3091469216
.1.28.1889.9744.66529.1348969.23694911.264853947.3362921639.52055334454
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) = a(n-1) +7*a(n-3) +a(n-5) -4*a(n-6)
k=4: a(n) = a(n-1) +12*a(n-3) +2*a(n-4) +2*a(n-5) -7*a(n-6) -a(n-7)
k=5: [order 20]
k=6: [order 37]
k=7: [order 81]
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +a(n-3) +4*a(n-4)
n=3: a(n) = a(n-1) +3*a(n-3) +8*a(n-4) +a(n-5) -a(n-6)
n=4: [order 12]
n=5: [order 29]
n=6: [order 59]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..1..0..1
..0..1..1..1. .0..1..1..0. .1..1..0..0. .0..1..1..0. .0..0..1..0
..0..0..1..0. .1..1..0..0. .1..1..0..0. .0..0..0..0. .0..0..0..0
CROSSREFS
Column 2 is A000930(n+1).
Sequence in context: A178234 A344440 A259175 * A346083 A301922 A144510
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 30 2017
STATUS
approved