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A268995
T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
14
2, 4, 4, 7, 13, 8, 13, 35, 41, 16, 23, 103, 174, 126, 32, 41, 278, 805, 849, 379, 64, 72, 763, 3331, 6009, 4083, 1121, 128, 126, 2037, 14080, 37987, 43512, 19416, 3272, 256, 219, 5421, 57287, 244397, 421450, 308112, 91491, 9449, 512, 379, 14264, 232449, 1506570
OFFSET
1,1
COMMENTS
Table starts
....2.....4.......7........13..........23............41..............72
....4....13......35.......103.........278...........763............2037
....8....41.....174.......805........3331.........14080...........57287
...16...126.....849......6009.......37987........244397.........1506570
...32...379....4083.....43512......421450.......4097199........38241770
...64..1121...19416....308112.....4583103......66954420.......946498448
..128..3272...91491...2144780....49084071....1073436321.....22995344760
..256..9449..427863..14730784...519385102...16957258387....550731432312
..512.27049.1988142.100087792..5442503771..264744926212..13040291111728
.1024.76866.9187653.674045392.56571775611.4093941136805.305911647779632
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)
k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7
k=5: [order 8] for n>9
k=6: [order 10] for n>12
k=7: [order 14] for n>16
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)
n=3: [order 9]
n=4: [order 16]
n=5: [order 26]
n=6: [order 42]
n=7: [order 68]
EXAMPLE
Some solutions for n=4 k=4
..1..1..0..1. .1..0..0..1. .0..0..0..0. .0..0..1..0. .0..0..0..1
..0..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..1..0. .0..0..0..1
..0..1..0..1. .0..0..0..0. .0..1..0..1. .1..0..0..0. .0..0..1..0
..0..0..0..0. .1..0..1..0. .0..0..0..0. .1..0..1..0. .1..0..1..0
CROSSREFS
Column 1 is A000079.
Row 1 is A208354(n+1).
Sequence in context: A224409 A226870 A227751 * A205744 A237859 A240338
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 17 2016
STATUS
approved