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A251268 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having x11-x00 less than x10-x01.

%I A251268 #6 Jun 02 2025 10:20:11
%S A251268 11,26,35,57,114,108,120,313,480,337,247,772,1667,2058,1049,502,1775,
%T A251268 4930,9109,8812,3268,1013,3894,13052,32636,49872,37772,10179,2036,
%U A251268 8277,31936,100843,217634,273607,161906,31707,4083,17224,73805,279718,790734
%N A251268 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having x11-x00 less than x10-x01.
%C A251268 Table starts
%C A251268 .....11.......26........57........120.........247..........502.........1013
%C A251268 .....35......114.......313........772........1775.........3894.........8277
%C A251268 ....108......480......1667.......4930.......13052........31936........73805
%C A251268 ....337.....2058......9109......32636......100843.......279718.......715685
%C A251268 ...1049.....8812.....49872.....217634......790734......2510004......7189937
%C A251268 ...3268....37772....273607....1457326.....6247708.....22806904.....73607411
%C A251268 ..10179...161906...1501739....9772880....49523566....208452452....760734085
%C A251268 ..31707...694042...8244503...65582500...393172015...1910905110...7901650053
%C A251268 ..98764..2975162..45265163..440223510..3123669457..17543333688..82288916360
%C A251268 .307641.12753740.248529844.2955392154.24825649060.161181383956.858174176431
%H A251268 R. H. Hardin, <a href="/A251268/b251268.txt">Table of n, a(n) for n = 1..479</a>
%F A251268 Empirical for column k:
%F A251268 k=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-3)
%F A251268 k=2: a(n) = 5*a(n-1) -2*a(n-2) -5*a(n-3) +2*a(n-4)
%F A251268 k=3: [order 10]
%F A251268 k=4: [order 16]
%F A251268 k=5: [order 36]
%F A251268 k=6: [order 62]
%F A251268 Empirical for row n:
%F A251268 n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3)
%F A251268 n=2: a(n) = 6*a(n-1) -14*a(n-2) +16*a(n-3) -9*a(n-4) +2*a(n-5)
%F A251268 n=3: [order 8]
%F A251268 n=4: [order 10]
%F A251268 n=5: [order 12]
%F A251268 n=6: [order 14]
%F A251268 n=7: [order 16]
%e A251268 Some solutions for n=4 k=4
%e A251268 ..0..0..0..0..0....0..1..1..1..1....0..0..0..0..1....0..0..1..0..1
%e A251268 ..1..1..1..1..1....0..0..0..1..1....0..1..1..1..1....0..0..0..1..1
%e A251268 ..1..1..1..1..1....1..1..1..1..1....0..0..0..0..0....0..1..1..1..1
%e A251268 ..1..1..1..1..1....0..0..0..0..0....0..0..1..1..1....0..0..0..0..0
%e A251268 ..0..0..0..0..1....0..0..1..1..1....0..1..0..1..1....0..0..1..1..1
%Y A251268 Column 1 is A052550(n+2)
%Y A251268 Row 1 is A000295(n+3)
%K A251268 nonn,tabl
%O A251268 1,1
%A A251268 _R. H. Hardin_, Dec 01 2014