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%I #7 Jan 14 2017 01:40:19
%S 2,5,5,16,24,16,58,156,156,58,214,1123,1986,1123,214,784,8268,28192,
%T 28192,8268,784,2880,60569,411825,782948,411825,60569,2880,10704,
%U 446426,6045460,22581061,22581061,6045460,446426,10704,40264,3333345,89538170
%N T(n,k) = 1/4 the number of (n+1) X (k+1) binary arrays with equal numbers of 2 X 2 subblocks with sums 1 and 3.
%C Table starts
%C ......2.........5...........16..............58................214
%C ......5........24..........156............1123...............8268
%C .....16.......156.........1986...........28192.............411825
%C .....58......1123........28192..........782948...........22581061
%C ....214......8268.......411825........22581061.........1291076970
%C ....784.....60569......6045460.......661355087........75369979530
%C ...2880....446426.....89538170.....19597196907......4461217004146
%C ..10704...3333345...1339793447....586441134417....266823559411796
%C ..40264..25146354..20215904926..17688240987365..16087490826015621
%C .152728.190958245.306972320468.536871796215114.976144514798586404
%H R. H. Hardin, <a href="/A184604/b184604.txt">Table of n, a(n) for n = 1..180</a>
%e Some solutions for 4 X 3:
%e ..1..0..0....0..0..1....1..1..1....1..0..1....0..0..0....1..0..0....1..0..0
%e ..1..1..0....1..1..1....0..0..1....0..1..1....1..0..1....0..0..1....0..1..0
%e ..0..0..1....0..0..0....0..0..0....0..1..1....0..1..1....1..1..1....0..1..1
%e ..1..1..0....1..1..0....1..1..1....0..0..0....0..1..0....0..1..1....0..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 18 2011