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A235449 T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with the difference between each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.

%I A235449 #6 Jun 26 2025 14:49:23
%S A235449 16,58,58,208,382,208,742,2476,2476,742,2644,15936,28962,15936,2644,
%T A235449 9418,102376,335898,335898,102376,9418,33544,657290,3886120,7017768,
%U A235449 3886120,657290,33544,119470,4219322,44920240,146213244,146213244,44920240
%N A235449 T(n,k) = Number of (n+1) X (k+1) 0..1 arrays with the difference between each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.
%C A235449 Table starts
%C A235449 ......16.........58..........208.............742...............2644
%C A235449 ......58........382.........2476...........15936.............102376
%C A235449 .....208.......2476........28962..........335898............3886120
%C A235449 .....742......15936.......335898.........7017768..........146213244
%C A235449 ....2644.....102376......3886120.......146213244.........5485253042
%C A235449 ....9418.....657290.....44920240......3043145826.......205551169550
%C A235449 ...33544....4219322....519099694.....63315473350......7699719982722
%C A235449 ..119470...27083638...5998218844...1317184566572....288383414393138
%C A235449 ..425500..173846264..69307887110..27401048899854..10800536489561114
%C A235449 .1515442.1115891712.800828757910.570010121664030.404495358726610494
%H A235449 R. H. Hardin, <a href="/A235449/b235449.txt">Table of n, a(n) for n = 1..144</a>
%F A235449 Empirical for column k:
%F A235449 k=1: a(n) = 4*a(n-1) -a(n-2) -2*a(n-3);
%F A235449 k=2: a(n) = 8*a(n-1) -8*a(n-2) -16*a(n-3) +12*a(n-4) +14*a(n-5) -a(n-6) -2*a(n-7);
%F A235449 k=3: [order 19];
%F A235449 k=4: [order 53].
%e A235449 Some solutions for n=3, k=4
%e A235449 ..0..0..0..1..0....0..0..1..0..1....0..0..0..0..0....0..0..1..0..1
%e A235449 ..0..1..1..1..0....0..0..0..1..1....1..1..0..1..0....0..1..0..1..0
%e A235449 ..1..1..0..1..0....0..0..1..0..0....0..0..0..1..0....0..1..0..0..1
%e A235449 ..0..0..1..0..0....0..1..1..1..1....0..1..0..1..0....0..0..0..1..0
%Y A235449 Column 1 is A180143(n+1).
%K A235449 nonn,tabl
%O A235449 1,1
%A A235449 _R. H. Hardin_, Jan 10 2014