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A275131 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.

%I A275131 #4 Jul 17 2016 11:01:42
%S A275131 1,2,1,5,4,2,14,16,12,4,41,64,45,36,8,122,256,174,129,108,16,365,1024,
%T A275131 675,568,373,324,32,1094,4096,2607,2545,2178,1083,972,64,3281,16384,
%U A275131 10077,11092,12423,8321,3148,2916,128,9842,65536,38967,48451,71576,62378
%N A275131 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,0) or (-1,1) and new values introduced in order 0..2.
%C A275131 Table starts
%C A275131 ...1.....2.....5......14.......41.......122.........365.........1094
%C A275131 ...1.....4....16......64......256......1024........4096........16384
%C A275131 ...2....12....45.....174......675......2607.......10077........38967
%C A275131 ...4....36...129.....568.....2545.....11092.......48451.......212897
%C A275131 ...8...108...373....2178....12423.....71576......412306......2381629
%C A275131 ..16...324..1083....8321....62378....473185.....3586068.....27224209
%C A275131 ..32...972..3148...31772...315021...3146574....31446544....315531602
%C A275131 ..64..2916..9157..121707..1591442..20970214...276145917...3669759648
%C A275131 .128..8748.26623..466252..8024937.139845553..2432426709..42807577389
%C A275131 .256.26244.77372.1783920.40445177.930732169.21443562178.499213473864
%H A275131 R. H. Hardin, <a href="/A275131/b275131.txt">Table of n, a(n) for n = 1..312</a>
%F A275131 Empirical for column k:
%F A275131 k=1: a(n) = 2*a(n-1) for n>2
%F A275131 k=2: a(n) = 3*a(n-1) for n>2
%F A275131 k=3: [order 9] for n>10
%F A275131 k=4: [order 17] for n>20
%F A275131 k=5: [order 28] for n>31
%F A275131 k=6: [order 67] for n>70
%F A275131 Empirical for row n:
%F A275131 n=1: a(n) = 4*a(n-1) -3*a(n-2)
%F A275131 n=2: a(n) = 4*a(n-1)
%F A275131 n=3: a(n) = 3*a(n-1) +2*a(n-2) +6*a(n-3) -2*a(n-4) -4*a(n-5) for n>6
%F A275131 n=4: [order 9] for n>11
%F A275131 n=5: [order 10] for n>14
%F A275131 n=6: [order 26] for n>28
%F A275131 n=7: [order 53] for n>58
%e A275131 Some solutions for n=4 k=4
%e A275131 ..0..0..1..1. .0..0..1..1. .0..1..2..2. .0..1..1..1. .0..0..1..2
%e A275131 ..2..2..0..2. .2..2..2..0. .2..0..1..0. .2..2..0..0. .1..2..0..1
%e A275131 ..1..1..1..1. .0..0..1..2. .1..2..2..2. .1..1..1..2. .0..1..2..2
%e A275131 ..0..0..0..0. .2..2..0..0. .0..1..1..1. .2..2..0..1. .2..0..0..1
%Y A275131 Column 1 is A000079(n-2).
%Y A275131 Column 2 is A003946(n-1).
%Y A275131 Row 1 is A007051(n-1).
%Y A275131 Row 2 is A000302(n-1).
%K A275131 nonn,tabl
%O A275131 1,2
%A A275131 _R. H. Hardin_, Jul 17 2016