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%I #7 Mar 02 2023 11:47:27
%S 2,4,4,8,9,8,16,25,16,16,32,64,48,25,32,64,169,144,81,36,64,128,441,
%T 432,256,120,49,128,256,1156,1296,841,400,169,64,256,512,3025,3888,
%U 2704,1360,576,224,81,512,1024,7921,11664,8836,4624,2025,784,289,100,1024,2048
%N T(n,k) = number of n X k binary arrays without the pattern 0 1 diagonally or antidiagonally.
%C Table starts
%C ....2...4...8...16...32....64...128....256.....512....1024.....2048.....4096
%C ....4...9..25...64..169...441..1156...3025....7921...20736....54289...142129
%C ....8..16..48..144..432..1296..3888..11664...34992..104976...314928...944784
%C ...16..25..81..256..841..2704..8836..28561...93025..301401...980100..3179089
%C ...32..36.120..400.1360..4624.15776..53824..183744..627264..2141568..7311616
%C ...64..49.169..576.2025..7056.24964..87616..310249.1092025..3865156.13623481
%C ..128..64.224..784.2800.10000.36000.129600..468000.1690000..6110000.22090000
%C ..256..81.289.1024.3721.13456.49284.179776..660969.2421136..8916196.32729841
%C ..512.100.360.1296.4752.17424.64416.238144..884256.3283344.12220128.45481536
%C .1024.121.441.1600.5929.21904.81796.304704.1142761.4276624.16080100.60341824
%H R. H. Hardin, <a href="/A188824/b188824.txt">Table of n, a(n) for n = 1..1627</a>
%F Empirical: a(n,1) = 2^n
%F Empirical: a(n,2) = n^2 + 2*n + 1
%F Empirical: a(n,3) = 2*a(n-1,3) - 2*a(n-3,3) + a(n-4,3)
%F Empirical: a(n,4) = 16*n^2
%F Empirical: a(n,5) = 2*a(n-1,5) - 2*a(n-3,5) + a(n-4,5) for n>5
%F Empirical: a(n,6) = 256*n^2 - 384*n + 144 for n>2
%F Empirical: a(n,7) = 2*a(n-1,7) - 2*a(n-3,7) + a(n-4,7) for n>7
%F Empirical: a(n,8) = 4096*n^2 - 11264*n + 7744 for n>4
%e Some solutions for 5X3
%e ..1..1..1....1..1..1....1..1..1....1..1..1....1..1..1....0..1..0....1..1..1
%e ..1..1..1....0..1..1....1..0..1....1..1..1....1..1..1....1..0..1....1..1..1
%e ..1..1..1....0..0..1....0..1..0....1..1..1....0..1..0....0..1..0....0..1..1
%e ..1..1..1....0..0..0....0..0..0....0..0..0....0..0..0....1..0..1....1..0..1
%e ..1..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..1..0
%Y Column 2 is A000290(n+1).
%Y Column 4 is A016802.
%Y Row 2 is A007598(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Apr 11 2011
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