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%I #22 Nov 19 2021 10:55:41
%S 7,13,13,25,33,25,49,81,81,49,97,209,257,209,97,193,529,833,833,529,
%T 193,385,1361,2689,3473,2689,1361,385,769,3473,8705,14145,14145,8705,
%U 3473,769,1537,8913,28161,58449,73345,58449,28161,8913,1537,3073,22801,91137
%N T(n,k) is the number of (n+1) X (k+1) 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
%C This is A183688+1 (the +1 comes from the all-1 matrix). [Discovered by Sequence Machine] - _Andrey Zabolotskiy_, Oct 19 2021
%H R. H. Hardin, <a href="/A204713/b204713.txt">Table of n, a(n) for n = 1..760</a>
%H Jon Maiga, <a href="http://sequencedb.net/s/A204713">Computer-generated formulas for A204713</a>, Sequence Machine.
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -2*a(n-2)
%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3)
%F k=3: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3)
%F k=4: a(n) = a(n-1) +13*a(n-2) +3*a(n-3) -16*a(n-4)
%F k=5: a(n) = 4*a(n-1) +15*a(n-2) -38*a(n-3) -52*a(n-4) +72*a(n-5)
%F k=6: (order 9 recurrence)
%F k=7: (order 10 recurrence)
%e Table starts
%e 7 13 25 49 97 193 385 769 1537
%e 13 33 81 209 529 1361 3473 8913 22801
%e 25 81 257 833 2689 8705 28161 91137 294913
%e 49 209 833 3473 14145 58449 239425 986129 4047681
%e 97 529 2689 14145 73345 382849 1992321 10382977 54072961
%e 193 1361 8705 58449 382849 2542369 16748161 110871041 731709057
%e 385 3473 28161 239425 1992321 16748161 140090241 1174759297 9838208513
%e 769 8913 91137 986129 10382977 110871041 1174759297 12503757969 132720731393
%e Some solutions for n=4 k=3
%e 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 1 0 1
%e 0 1 0 1 0 1 0 1 1 0 1 0 0 1 0 1 1 1 1 0
%e 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 0 1 0 1 1
%e 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 0
%e 1 1 1 0 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1
%Y Column 1 is A004119(n+1).
%Y Cf. A183688.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 18 2012
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