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A235679 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise.

%I A235679 #6 Jul 23 2025 08:44:24
%S A235679 16,58,58,208,380,208,742,2456,2456,742,2644,15790,28584,15790,2644,
%T A235679 9418,101398,330840,330840,101398,9418,33544,650928,3824528,6894210,
%U A235679 3824528,650928,33544,119470,4178316,44196144,143484144,143484144,44196144
%N A235679 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference between each 2X2 subblock maximum and minimum lexicographically nondecreasing columnwise and nonincreasing rowwise.
%C A235679 Table starts
%C A235679 ......16.........58..........208.............742...............2644
%C A235679 ......58........380.........2456...........15790.............101398
%C A235679 .....208.......2456........28584..........330840............3824528
%C A235679 .....742......15790.......330840.........6894210..........143484144
%C A235679 ....2644.....101398......3824528.......143484144.........5376199876
%C A235679 ....9418.....650928.....44196144......2985166430.......201368802704
%C A235679 ...33544....4178316....510685176.....62100488254......7541722428052
%C A235679 ..119470...26820102...5900818062...1291848133836....282448223982692
%C A235679 ..425500..172154058..68181837738..26873571586520..10578025710796398
%C A235679 .1515442.1105028596.787815537064.559034577488572.396159194076516486
%H A235679 R. H. Hardin, <a href="/A235679/b235679.txt">Table of n, a(n) for n = 1..220</a>
%F A235679 Empirical for column k:
%F A235679 k=1: a(n) = 4*a(n-1) -a(n-2) -2*a(n-3)
%F A235679 k=2: a(n) = 8*a(n-1) -9*a(n-2) -9*a(n-3) +10*a(n-4) +3*a(n-5) -2*a(n-6)
%F A235679 k=3: [order 11]
%F A235679 k=4: [order 22]
%F A235679 k=5: [order 46]
%F A235679 k=6: [order 87]
%e A235679 Some solutions for n=3 k=4
%e A235679 ..0..0..1..0..0....0..0..1..1..0....0..1..0..0..1....0..0..1..0..0
%e A235679 ..1..0..0..1..1....1..0..1..0..1....0..1..0..1..1....1..0..1..0..1
%e A235679 ..1..1..0..1..0....1..0..0..1..0....0..0..0..1..0....1..0..0..1..0
%e A235679 ..1..1..0..0..0....1..1..0..0..1....0..0..0..0..0....0..0..1..1..1
%Y A235679 Column 1 is A180143(n+1)
%K A235679 nonn,tabl
%O A235679 1,1
%A A235679 _R. H. Hardin_, Jan 13 2014