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A227385 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.

%I A227385 #6 Jul 23 2025 05:36:44
%S A227385 2,3,3,4,7,4,5,15,15,5,6,30,54,30,6,7,56,185,185,56,7,8,98,587,1104,
%T A227385 587,98,8,9,162,1704,6160,6160,1704,162,9,10,255,4532,31073,61127,
%U A227385 31073,4532,255,10,11,385,11126,141192,550010,550010,141192,11126,385,11,12,561
%N A227385 T(n,k)=Number of nXk 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(k+1) binary array having a sum of one, with rows and columns of the latter in lexicographically nondecreasing order.
%C A227385 Table starts
%C A227385 ..2...3.....4.......5.........6...........7...........8...........9..........10
%C A227385 ..3...7....15......30........56..........98.........162.........255.........385
%C A227385 ..4..15....54.....185.......587........1704........4532.......11126.......25430
%C A227385 ..5..30...185....1104......6160.......31073......141192......581706.....2192737
%C A227385 ..6..56...587....6160.....61127......550010.....4450124....32473856...215116595
%C A227385 ..7..98..1704...31073....550010.....8988949...133142369..1779353333.21501389691
%C A227385 ..8.162..4532..141192...4450124...133142369..3657501287.91016881301
%C A227385 ..9.255.11126..581706..32473856..1779353333.91016881301
%C A227385 .10.385.25430.2192737.215116595.21501389691
%H A227385 R. H. Hardin, <a href="/A227385/b227385.txt">Table of n, a(n) for n = 1..111</a>
%F A227385 Empirical for column k:
%F A227385 k=1: a(n) = n + 1
%F A227385 k=2: a(n) = (1/24)*n^4 + (1/12)*n^3 + (11/24)*n^2 + (17/12)*n + 1
%F A227385 k=3: [polynomial of degree 9] for n>3
%F A227385 k=4: [polynomial of degree 19] for n>7
%F A227385 k=5: [polynomial of degree 39] for n>22
%e A227385 Some solutions for n=4 k=4
%e A227385 ..1..0..0..0....0..0..0..1....1..0..0..0....0..0..1..0....0..0..1..0
%e A227385 ..0..0..1..0....1..0..0..0....0..0..1..0....0..1..0..1....0..1..0..0
%e A227385 ..0..0..1..1....0..0..0..0....0..0..1..0....1..0..1..1....1..0..1..0
%e A227385 ..0..0..1..1....0..0..0..1....0..0..0..0....0..1..0..1....0..1..1..1
%Y A227385 Column 2 is A055795(n+2)
%K A227385 nonn,tabl
%O A227385 1,1
%A A227385 _R. H. Hardin_ Jul 09 2013