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A250797 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.

%I A250797 #6 Jul 23 2025 12:46:10
%S A250797 10,24,24,54,66,58,118,162,180,140,252,376,482,490,338,530,838,1190,
%T A250797 1430,1336,816,1102,1818,2776,3776,4258,3646,1970,2272,3868,6230,9258,
%U A250797 12062,12706,9956,4756,4654,8114,13598,21610,31220,38676,37986,27194,11482
%N A250797 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
%C A250797 Table starts
%C A250797 ....10.....24......54.....118......252......530......1102......2272......4654
%C A250797 ....24.....66.....162.....376......838.....1818......3868......8114.....16842
%C A250797 ....58....180.....482....1190.....2776.....6230.....13598.....29084.....61274
%C A250797 ...140....490....1430....3776.....9258....21610.....48600....106426....228342
%C A250797 ...338...1336....4258...12062....31220....76110....177142....398704....874298
%C A250797 ...816...3646...12706...38676...105954...270598....653880...1517666...3411886
%C A250797 ..1970...9956...37986..124366...361344...968942...2437366...5849556..13519146
%C A250797 ..4756..27194..113694..400616..1236058..3485538...9144752..22741458..54152230
%C A250797 .11482..74288..340562.1292134..4237556.12580830..34478398..88996688.218754226
%C A250797 .27720.202950.1020650.4171276.14549610.45517150.130446176.349951066.889238238
%H A250797 R. H. Hardin, <a href="/A250797/b250797.txt">Table of n, a(n) for n = 1..480</a>
%F A250797 Empirical for column k:
%F A250797 k=1: a(n) = 2*a(n-1) +a(n-2)
%F A250797 k=2: a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +2*a(n-4)
%F A250797 k=3: a(n) = 6*a(n-1) -10*a(n-2) +11*a(n-4) -6*a(n-5)
%F A250797 k=4: a(n) = 8*a(n-1) -20*a(n-2) +8*a(n-3) +33*a(n-4) -36*a(n-5) +8*a(n-7)
%F A250797 k=5: [order 9]
%F A250797 k=6: [order 11]
%F A250797 k=7: [order 13]
%F A250797 Empirical for row n:
%F A250797 n=1: a(n) = 3*a(n-1) -a(n-2) -2*a(n-3)
%F A250797 n=2: a(n) = 4*a(n-1) -4*a(n-2) -a(n-3) +2*a(n-4)
%F A250797 n=3: a(n) = 5*a(n-1) -8*a(n-2) +3*a(n-3) +3*a(n-4) -2*a(n-5)
%F A250797 n=4: a(n) = 4*a(n-1) -2*a(n-2) -9*a(n-3) +9*a(n-4) +6*a(n-5) -8*a(n-6) -a(n-7) +2*a(n-8)
%F A250797 n=5: [order 9]
%F A250797 n=6: [order 12]
%F A250797 n=7: [order 13]
%e A250797 Some solutions for n=4 k=4
%e A250797 ..0..0..0..1..0....0..0..0..0..0....1..1..1..0..1....0..0..0..0..1
%e A250797 ..0..0..0..0..1....0..0..0..0..0....1..1..1..0..0....0..0..0..0..0
%e A250797 ..0..0..0..0..1....0..0..0..0..1....1..1..1..0..1....0..0..0..0..0
%e A250797 ..1..1..1..1..0....0..0..0..0..1....1..1..1..0..1....0..0..1..1..1
%e A250797 ..1..1..1..1..0....0..0..0..0..0....1..1..1..0..1....0..0..1..1..1
%Y A250797 Column 1 is A052542(n+2)
%K A250797 nonn,tabl
%O A250797 1,1
%A A250797 _R. H. Hardin_, Nov 27 2014