|
%I #4 Jan 24 2016 14:10:13
%S 3,9,9,27,81,24,78,729,576,63,222,6084,13824,3969,159,622,49284,
%T 295962,250047,25281,394,1722,386884,6042732,13530274,4019679,155236,
%U 957,4719,2965284,117582228,687233742,528293442,61162984,915849,2292,12821
%N T(n,k)=Number of nXk 0..2 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.
%C Table starts
%C .....3.........9............27..............78...............222
%C .....9........81...........729............6084.............49284
%C ....24.......576.........13824..........295962...........6042732
%C ....63......3969........250047........13530274.........687233742
%C ...159.....25281.......4019679.......528293442.......64075543999
%C ...394....155236......61162984.....19177213020.....5458407864352
%C ...957....915849.....876467493....642612340592...420621575011611
%C ..2292...5253264...12040481088..20358126145678.30224756956473940
%C ..5419..29365561..159131975059.612589053437088
%C .12678.160731684.2037756289752
%H R. H. Hardin, <a href="/A268026/b268026.txt">Table of n, a(n) for n = 1..84</a>
%F Empirical for column k:
%F k=1: a(n) = 6*a(n-1) -9*a(n-2) -8*a(n-3) +24*a(n-4) -16*a(n-6)
%F k=2: [order 15]
%F k=3: [order 28]
%F Empirical for row n:
%F n=1: a(n) = 6*a(n-1) -9*a(n-2) -4*a(n-3) +9*a(n-4) +6*a(n-5) +a(n-6)
%F n=2: [order 15]
%F n=3: [order 86] for n>87
%e Some solutions for n=3 k=4
%e ..0..0..2..2....0..2..1..1....0..0..1..2....0..1..2..0....0..2..2..1
%e ..2..2..0..1....0..1..0..0....2..0..0..1....1..0..1..2....1..2..0..0
%e ..0..0..0..1....2..2..2..0....0..2..0..1....2..1..1..1....0..1..1..2
%Y Column 1 is A267960.
%Y Column 2 is A267961.
%Y Row 1 is A268013.
%Y Row 2 is A268014.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 24 2016
| 