|
%I #4 Nov 29 2014 18:39:51
%S 27,83,83,192,284,192,420,616,616,420,872,1306,1165,1306,872,1782,
%T 2534,2362,2362,2534,1782,3593,4848,4379,4718,4379,4848,3593,7215,
%U 9086,8284,8512,8512,8284,9086,7215,14443,17102,15411,15780,14891,15780,15411
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements
%C Table starts
%C ....27....83....192....420....872...1782...3593....7215...14443...28891...57762
%C ....83...284....616...1306...2534...4848...9086...17102...32336...61836..119420
%C ...192...616...1165...2362...4379...8284..15411...29142...55429..106880..207889
%C ...420..1306...2362...4718...8512..15780..28616...52934...98550..186788..358250
%C ...872..2534...4379...8512..14891..27040..48017...87488..160737..301824..574763
%C ..1782..4848...8284..15780..27040..47932..82898..147152..263698..484744..907152
%C ..3593..9086..15411..28616..48017..82898.139553..240972..420611..755534.1387095
%C ..7215.17102..29142..52934..87488.147152.240972..402854..680446.1184344.2115062
%C .14443.32336..55429..98550.160737.263698.420611..680446.1109887.1863898.3220133
%C .28891.61836.106880.186788.301824.484744.755534.1184344.1863898.3007772.4993492
%H R. H. Hardin, <a href="/A251088/b251088.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical for column k:
%F k=1: a(n) = 5*a(n-1) -8*a(n-2) +2*a(n-3) +7*a(n-4) -7*a(n-5) +2*a(n-6) for n>7
%F k=2: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%F k=3: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%F k=4: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%F k=5: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%F k=6: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%F k=7: a(n) = 6*a(n-1) -13*a(n-2) +10*a(n-3) +5*a(n-4) -14*a(n-5) +9*a(n-6) -2*a(n-7) for n>8
%e Some solutions for n=4 k=4
%e ..0..0..1..1..2....0..1..1..1..2....0..1..2..2..2....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....2..2..2..2..2
%e ..1..1..1..1..1....0..0..0..0..1....2..2..2..2..2....0..0..0..0..0
%e ..0..0..0..0..0....0..0..0..0..1....0..0..0..0..0....1..1..1..1..1
%e ..1..1..1..0..0....2..1..0..0..0....2..2..2..1..1....0..0..0..0..0
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 29 2014
| 