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A269075 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two not more than once. 13
2, 4, 4, 7, 11, 8, 13, 27, 32, 16, 23, 76, 123, 89, 32, 41, 185, 521, 537, 244, 64, 72, 489, 1887, 3288, 2343, 659, 128, 126, 1204, 7477, 17713, 20400, 10167, 1760, 256, 219, 3059, 27042, 102545, 165607, 123976, 43959, 4657, 512, 379, 7539, 102070, 542112 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
....2.....4.......7........13..........23...........41.............72
....4....11......27........76.........185..........489...........1204
....8....32.....123.......521........1887.........7477..........27042
...16....89.....537......3288.......17713.......102545.........542112
...32...244....2343.....20400......165607......1383105.......10778640
...64...659...10167....123976.....1529241.....18220241......210476400
..128..1760...43959....742688....14011359....236272677.....4064720816
..256..4657..189465...4397376...127528641...3024972401....77785162880
..512.12228..814359..25791040..1154377943..38333973609..1477636398784
.1024.31899.3491691.150081504.10400164377.481701017577.27897108860960
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 4*a(n-1) -2*a(n-2) -4*a(n-3) -a(n-4)
k=3: a(n) = 10*a(n-1) -31*a(n-2) +24*a(n-3) +21*a(n-4) -18*a(n-5) -9*a(n-6)
k=4: a(n) = 12*a(n-1) -40*a(n-2) +8*a(n-3) +92*a(n-4) -32*a(n-5) -64*a(n-6) for n>7
k=5: [order 12]
k=6: [order 14]
k=7: [order 24] for n>25
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) -6*a(n-3) -9*a(n-4)
n=3: a(n) = 4*a(n-1) +8*a(n-2) -34*a(n-3) -16*a(n-4) +60*a(n-5) -25*a(n-6)
n=4: [order 8]
n=5: [order 14]
EXAMPLE
Some solutions for n=4 k=4
..1..0..0..0. .0..1..1..0. .1..0..0..1. .0..0..0..1. .0..1..0..1
..0..0..0..0. .0..0..0..0. .1..0..1..0. .0..0..0..1. .0..1..0..1
..1..0..0..0. .1..0..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..0..0..1. .1..0..0..1. .0..0..0..0. .1..0..1..0. .0..0..0..1
CROSSREFS
Column 1 is A000079.
Column 2 is A268744.
Row 1 is A208354(n+1).
Sequence in context: A295275 A295253 A295652 * A283543 A297682 A297607
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 19 2016
STATUS
approved

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Last modified March 2 02:30 EST 2024. Contains 370447 sequences. (Running on oeis4.)