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A204713 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.

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