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A281605 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.

%I A281605 #4 Jan 25 2017 10:40:46
%S A281605 1,2,2,4,9,5,11,29,50,14,30,110,209,285,41,82,442,1283,1623,1617,122,
%T A281605 224,1708,8180,16198,12413,9188,365,612,6596,49572,167545,203276,
%U A281605 95623,52193,1094,1672,25624,302304,1626073,3401430,2563481,736757,296511,3281,4568
%N A281605 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
%C A281605 Table starts
%C A281605 ....1.......2.........4..........11.............30.............82
%C A281605 ....2.......9........29.........110............442...........1708
%C A281605 ....5......50.......209........1283...........8180..........49572
%C A281605 ...14.....285......1623.......16198.........167545........1626073
%C A281605 ...41....1617.....12413......203276........3401430.......52899445
%C A281605 ..122....9188.....95623.....2563481.......69506779.....1732267694
%C A281605 ..365...52193....736757....32354824.....1421127262....56764280423
%C A281605 .1094..296511...5678559...408458506....29066686772..1860912910152
%C A281605 .3281.1684466..43771933..5156857179...594539026170.61012156448915
%C A281605 .9842.9569425.337417047.65107404580.12161158312943
%H A281605 R. H. Hardin, <a href="/A281605/b281605.txt">Table of n, a(n) for n = 1..112</a>
%F A281605 Empirical for column k:
%F A281605 k=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A281605 k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
%F A281605 k=3: a(n) = 7*a(n-1) +10*a(n-2) -26*a(n-3) -64*a(n-4) -40*a(n-5) for n>6
%F A281605 k=4: [order 16] for n>18
%F A281605 k=5: [order 40] for n>42
%F A281605 Empirical for row n:
%F A281605 n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
%F A281605 n=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
%F A281605 n=3: [order 13] for n>15
%F A281605 n=4: [order 55] for n>58
%e A281605 Some solutions for n=4 k=4
%e A281605 ..0..0..1..0. .0..1..0..2. .0..1..0..1. .0..1..2..2. .0..1..2..0
%e A281605 ..1..2..2..1. .0..1..0..2. .1..2..0..1. .0..1..0..1. .0..1..0..1
%e A281605 ..0..1..0..1. .2..2..0..1. .1..0..1..2. .0..1..2..1. .2..1..0..1
%e A281605 ..2..1..2..1. .0..1..0..2. .1..2..1..0. .1..2..0..1. .0..1..2..1
%Y A281605 Column 1 is A007051(n-1).
%Y A281605 Column 2 is A231413(n-1).
%Y A281605 Row 1 is A021006(n-3).
%Y A281605 Row 2 is A280853.
%K A281605 nonn,tabl
%O A281605 1,2
%A A281605 _R. H. Hardin_, Jan 25 2017