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A251128 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.

%I A251128 #8 Jul 23 2025 13:06:01
%S A251128 10,21,21,40,40,40,72,69,69,72,125,117,108,117,125,212,193,173,173,
%T A251128 193,212,354,315,272,266,272,315,354,585,510,430,401,401,430,510,585,
%U A251128 960,823,680,612,580,612,680,823,960,1568,1326,1080,938,854,854,938,1080,1326
%N A251128 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.
%C A251128 Table starts
%C A251128 ...10...21...40...72..125..212..354..585...960..1568..2553..4148..6730.10909
%C A251128 ...21...40...69..117..193..315..510..823..1326..2136..3442..5550..8955.14458
%C A251128 ...40...69..108..173..272..430..680.1080..1721..2752..4413..7093.11421.18415
%C A251128 ...72..117..173..266..401..612..938.1452..2266..3565..5646..8991.14379.23071
%C A251128 ..125..193..272..401..580..854.1268.1912..2921..4520..7069.11153.17717.28291
%C A251128 ..212..315..430..612..854.1214.1743.2550..3795..5747..8835.13757.21640.34309
%C A251128 ..354..510..680..938.1268.1743.2420.3429..4957..7321.11025.16890.26241.41224
%C A251128 ..585..823.1080.1452.1912.2550.3429.4702..6585..9447.13873.20817.31818.49369
%C A251128 ..960.1326.1721.2266.2921.3795.4957.6585..8926.12405.17694.25890.38762.59176
%C A251128 .1568.2136.2752.3565.4520.5747.7321.9447.12405.16680.23037.32726.47762.71410
%H A251128 R. H. Hardin, <a href="/A251128/b251128.txt">Table of n, a(n) for n = 1..1104</a>
%F A251128 Empirical for column k:
%F A251128 k=1: a(n) = 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4)
%F A251128 k=2: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5)
%F A251128 k=3: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%F A251128 k=4: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%F A251128 k=5: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%F A251128 k=6: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%F A251128 k=7: a(n) = 4*a(n-1) -5*a(n-2) +a(n-3) +2*a(n-4) -a(n-5) for n>6
%e A251128 Some solutions for n=4 k=4
%e A251128 ..0..1..1..1..1....0..0..0..1..1....0..0..1..0..1....1..0..0..0..1
%e A251128 ..0..0..0..0..0....0..0..0..1..0....1..0..1..0..1....1..0..0..0..1
%e A251128 ..1..1..1..1..1....0..0..0..1..0....1..0..1..0..1....1..0..0..0..0
%e A251128 ..0..0..0..0..0....0..0..0..1..0....1..0..1..0..1....1..0..0..0..0
%e A251128 ..0..0..0..0..0....1..1..0..1..0....1..0..1..0..0....1..0..0..0..0
%Y A251128 Column 1 is A001891(n+2)
%K A251128 nonn,tabl
%O A251128 1,1
%A A251128 _R. H. Hardin_, Nov 30 2014