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A251100 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.

%I A251100 #6 Jul 23 2025 13:04:17
%S A251100 13,41,41,129,212,129,406,1109,1109,406,1278,5817,9597,5817,1278,4023,
%T A251100 30517,82814,82814,30517,4023,12664,160086,713769,1175519,713769,
%U A251100 160086,12664,39865,839758,6151051,16697127,16697127,6151051,839758,39865
%N A251100 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having its minimum diagonal element less than its minimum antidiagonal element.
%C A251100 Table starts
%C A251100 .....13........41.........129...........406.............1278...............4023
%C A251100 .....41.......212........1109..........5817............30517.............160086
%C A251100 ....129......1109........9597.........82814...........713769............6151051
%C A251100 ....406......5817.......82814.......1175519.........16697127..........237288487
%C A251100 ...1278.....30517......713769......16697127........391088995.........9160138107
%C A251100 ...4023....160086.....6151051.....237288487.......9160138107.......353489877714
%C A251100 ..12664....839758....53009570....3372537762.....214512524583.....13640572890821
%C A251100 ..39865...4405079...456842112...47933018061....5023196973684....526395665662695
%C A251100 .125491..23107524..3937123328..681254534234..117627015646158..20314343818684906
%C A251100 .395033.121214121.33930621210.9682407527191.2754453306431041.783961045672945429
%H A251100 R. H. Hardin, <a href="/A251100/b251100.txt">Table of n, a(n) for n = 1..480</a>
%F A251100 Empirical for column k:
%F A251100 k=1: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3)
%F A251100 k=2: a(n) = 7*a(n-1) -11*a(n-2) +10*a(n-3) -3*a(n-4)
%F A251100 k=3: [order 9]
%F A251100 k=4: [order 17]
%F A251100 k=5: [order 31]
%F A251100 k=6: [order 57] for n>58
%e A251100 Some solutions for n=3 k=4
%e A251100 ..0..0..1..1..0....0..1..1..0..1....1..1..1..0..0....0..0..1..1..0
%e A251100 ..0..0..0..1..1....0..1..1..0..1....0..0..1..0..0....1..0..0..0..0
%e A251100 ..0..0..0..0..1....0..0..1..0..0....0..0..0..0..0....0..0..0..1..0
%e A251100 ..0..1..1..0..1....1..0..1..1..1....1..0..0..1..0....0..0..0..1..0
%Y A251100 Column 1 is A052529(n+2)
%K A251100 nonn,tabl
%O A251100 1,1
%A A251100 _R. H. Hardin_, Nov 29 2014