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A297582 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s. 13
1, 2, 1, 3, 5, 1, 4, 11, 9, 1, 6, 17, 36, 20, 1, 9, 39, 72, 102, 41, 1, 13, 93, 188, 254, 370, 85, 1, 19, 183, 688, 1017, 1104, 1243, 178, 1, 28, 373, 2085, 5263, 5800, 4428, 3854, 369, 1, 41, 823, 5497, 20771, 47968, 31171, 17549, 13078, 769, 1, 60, 1741, 16037, 76340 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
.1...2.....3......4.......6.........9.........13..........19............28
.1...5....11.....17......39........93........183.........373...........823
.1...9....36.....72.....188.......688.......2085........5497.........16037
.1..20...102....254....1017......5263......20771.......76340........320326
.1..41...370...1104....5800.....47968.....284289.....1400065.......8274627
.1..85..1243...4428...31171....395011....3355439....21941552.....181405030
.1.178..3854..17549..171543...3230902...38609160...348140132....4059598106
.1.369.13078..71541..945046..27481626..476513137..5752782514...94310855136
.1.769.43861.288624.5175491.229676841.5731862594.92802629660.2136636243308
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
k=3: a(n) = a(n-1) +2*a(n-2) +19*a(n-3) +4*a(n-4) -17*a(n-5) -8*a(n-6)
k=4: [order 16]
k=5: [order 30]
k=6: [order 57]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-3)
n=2: a(n) = a(n-1) +4*a(n-3) +2*a(n-4)
n=3: a(n) = a(n-1) +a(n-2) +8*a(n-3) +18*a(n-4) +a(n-5) -11*a(n-6) -12*a(n-7) -a(n-8)
n=4: [order 17]
n=5: [order 41]
n=6: [order 94]
EXAMPLE
Some solutions for n=5 k=4
..1..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..1. .0..1..1..0
..0..0..0..0. .0..0..1..0. .1..0..0..0. .0..1..1..0. .0..0..0..0
..0..0..1..0. .1..1..1..0. .1..0..0..0. .0..1..0..0. .0..1..0..0
..0..0..0..1. .1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..0
CROSSREFS
Column 2 is A105309(n+1).
Row 1 is A000930(n+1).
Sequence in context: A118243 A210233 A347667 * A134081 A134247 A210225
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 01 2018
STATUS
approved

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Last modified February 25 10:08 EST 2024. Contains 370315 sequences. (Running on oeis4.)