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A297607
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 1 or 3 neighboring 1s.
13
2, 4, 4, 7, 11, 8, 13, 35, 35, 16, 24, 96, 181, 106, 32, 44, 281, 787, 953, 327, 64, 81, 829, 3691, 6413, 4997, 1003, 128, 149, 2428, 17186, 49198, 52512, 26155, 3082, 256, 274, 7059, 80140, 368007, 654033, 429491, 137033, 9465, 512, 504, 20611, 371557
OFFSET
1,1
COMMENTS
Table starts
...2.....4.......7........13..........24............44..............81
...4....11......35........96.........281...........829............2428
...8....35.....181.......787........3691.........17186...........80140
..16...106.....953......6413.......49198........368007.........2781983
..32...327....4997.....52512......654033.......7847849........95770934
..64..1003...26155....429491.....8689859.....167209522......3295502717
.128..3082..137033...3514058...115571432....3567494618....113592447685
.256..9465..717905..28752016..1536728161...76095857063...3914150992637
.512.29073.3760657.235246416.20433704585.1623142226575.134873268392766
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +3*a(n-2) +a(n-3) -a(n-5)
k=3: [order 11]
k=4: [order 32]
k=5: [order 55]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2) +a(n-3)
n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3) +12*a(n-4) -12*a(n-6)
n=3: [order 13]
n=4: [order 34]
n=5: [order 96]
EXAMPLE
Some solutions for n=4 k=4
..1..0..1..0. .0..0..1..0. .0..0..0..1. .0..0..1..0. .1..0..1..1
..0..0..1..0. .1..0..0..1. .1..0..1..0. .0..0..0..1. .1..0..0..0
..0..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..0..0. .0..0..0..1
..1..0..1..1. .0..1..0..1. .0..0..1..1. .0..1..0..0. .0..1..1..1
CROSSREFS
Column 1 is A000079.
Column 2 is A295247.
Row 1 is A000073(n+3).
Sequence in context: A269075 A283543 A297682 * A223770 A223777 A227089
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 01 2018
STATUS
approved