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A228506 T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally. 11

%I #7 Sep 01 2013 17:48:59

%S 1,1,1,2,1,2,3,3,3,3,5,5,12,5,5,8,11,29,29,11,8,13,21,88,87,88,21,13,

%T 21,43,239,358,358,239,43,21,34,85,684,1252,2002,1252,684,85,34,55,

%U 171,1909,4749,9528,9528,4749,1909,171,55,89,341,5392,17285,49101,59839,49101

%N T(n,k)=Number of nXk binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.

%C Table starts

%C ..1...1....2.....3.......5........8........13.........21..........34

%C ..1...1....3.....5......11.......21........43.........85.........171

%C ..2...3...12....29......88......239.......684.......1909........5392

%C ..3...5...29....87.....358.....1252......4749......17285.......64235

%C ..5..11...88...358....2002.....9528.....49101.....243118.....1228036

%C ..8..21..239..1252....9528....59839....413786....2724191....18387032

%C .13..43..684..4749...49101...413786...3862849...34229311...311423874

%C .21..85.1909.17285..243118..2724191..34229311..405580157..4951454523

%C .34.171.5392.64235.1228036.18387032.311423874.4951454523.81304395949

%H R. H. Hardin, <a href="/A228506/b228506.txt">Table of n, a(n) for n = 1..1740</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = a(n-1) +2*a(n-2)

%F k=3: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3)

%F k=4: a(n) = 2*a(n-1) +7*a(n-2) -2*a(n-3) -3*a(n-4)

%F k=5: a(n) = 2*a(n-1) +16*a(n-2) +a(n-3) -27*a(n-4) +a(n-5) +4*a(n-6)

%F k=6: [order 8]

%F k=7: [order 14]

%e Some solutions for n=4 k=4

%e ..1..0..0..0....1..0..0..0....1..0..0..1....1..0..0..0....1..0..0..1

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..0....1..0..0..0....0..0..0..0....0..0..0..1....1..0..0..0

%e ..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..1..0

%Y Column 1 is A000045

%Y Column 2 is A001045

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_ Aug 23 2013

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Last modified June 24 00:02 EDT 2024. Contains 373661 sequences. (Running on oeis4.)