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A227025 T(n,k)=Number of nXk (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order.

%I A227025 #6 Jul 23 2025 05:32:29
%S A227025 3,7,7,12,26,12,18,72,72,18,25,171,335,171,25,33,368,1366,1366,368,33,
%T A227025 42,729,4948,10050,4948,729,42,52,1343,16115,65317,65317,16115,1343,
%U A227025 52,63,2325,47659,375270,786154,375270,47659,2325,63,75,3819,129463,1924848
%N A227025 T(n,k)=Number of nXk (0,1,2) arrays of permanents of 2X2 subblocks of some (n+1)X(k+1) binary array with rows and columns of the latter in lexicographically nondecreasing order.
%C A227025 Table starts
%C A227025 ..3....7.....12.......18.........25...........33............42............52
%C A227025 ..7...26.....72......171........368..........729..........1343..........2325
%C A227025 .12...72....335.....1366.......4948........16115.........47659........129463
%C A227025 .18..171...1366....10050......65317.......375270.......1924848.......8908719
%C A227025 .25..368...4948....65317.....786154......8379285......79224749.....668706345
%C A227025 .33..729..16115...375270....8379285....168973605....3034194621...48518491730
%C A227025 .42.1343..47659..1924848...79224749...3034194621..104606988712.3220901001021
%C A227025 .52.2325.129463..8908719..668706345..48518491730.3220901001021
%C A227025 .63.3819.326522.37616613.5081503151.694140800875
%H A227025 R. H. Hardin, <a href="/A227025/b227025.txt">Table of n, a(n) for n = 1..112</a>
%F A227025 Empirical for column k:
%F A227025 k=1: a(n) = (1/2)*n^2 + (5/2)*n
%F A227025 k=2: [polynomial of degree 5] for n>2
%F A227025 k=3: [polynomial of degree 11] for n>6
%e A227025 Some solutions for n=4 k=4
%e A227025 ..0..0..0..2....0..0..1..1....1..0..0..0....0..0..1..1....0..0..1..0
%e A227025 ..0..0..1..1....1..0..1..1....0..0..0..0....0..2..1..1....0..1..0..0
%e A227025 ..1..0..1..1....1..0..1..1....1..1..0..1....0..2..2..1....2..0..0..1
%e A227025 ..0..0..1..0....2..2..2..1....2..1..0..1....1..2..1..0....2..0..0..1
%Y A227025 Column 1 is A027379
%K A227025 nonn,tabl
%O A227025 1,1
%A A227025 _R. H. Hardin_ Jun 27 2013