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A274803 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.

%I A274803 #4 Jul 07 2016 11:08:47
%S A274803 1,1,1,2,3,2,4,8,8,4,8,22,30,22,8,16,60,112,112,60,16,32,164,420,596,
%T A274803 420,164,32,64,448,1572,3104,3104,1572,448,64,128,1224,5888,16328,
%U A274803 22988,16328,5888,1224,128,256,3344,22048,85504,169328,169328,85504,22048,3344
%N A274803 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.
%C A274803 Table starts
%C A274803 ...1....1......2........4.........8..........16...........32.............64
%C A274803 ...1....3......8.......22........60.........164..........448...........1224
%C A274803 ...2....8.....30......112.......420........1572.........5888..........22048
%C A274803 ...4...22....112......596......3104.......16328........85504.........448656
%C A274803 ...8...60....420.....3104.....22988......169328......1252608........9243332
%C A274803 ..16..164...1572....16328....169328.....1774372.....18476064......193292660
%C A274803 ..32..448...5888....85504...1252608....18476064....273764292.....4044928780
%C A274803 ..64.1224..22048...448656...9243332...193292660...4044928780....85071335388
%C A274803 .128.3344..82568..2352080..68301192..2016460140..59936952948..1784175028356
%C A274803 .256.9136.309200.12335680.504334580.21072173792.886462457880.37524080122192
%H A274803 R. H. Hardin, <a href="/A274803/b274803.txt">Table of n, a(n) for n = 1..449</a>
%F A274803 Empirical for column k:
%F A274803 k=1: a(n) = 2*a(n-1) for n>2
%F A274803 k=2: a(n) = 2*a(n-1) +2*a(n-2)
%F A274803 k=3: a(n) = 2*a(n-1) +6*a(n-2) +2*a(n-3)
%F A274803 k=4: a(n) = 2*a(n-1) +15*a(n-2) +11*a(n-3) -2*a(n-4) -2*a(n-5)
%F A274803 k=5: a(n) = 2*a(n-1) +35*a(n-2) +42*a(n-3) -41*a(n-4) -60*a(n-5) -23*a(n-6) -2*a(n-7)
%F A274803 k=6: [order 14] for n>15
%F A274803 k=7: [order 25] for n>26
%e A274803 Some solutions for n=4 k=4
%e A274803 ..0..1..0..2. .0..1..2..0. .0..1..2..1. .0..1..2..1. .0..1..0..1
%e A274803 ..1..2..1..0. .1..0..1..2. .1..2..1..2. .1..0..1..0. .1..0..1..2
%e A274803 ..0..1..0..1. .0..1..2..1. .2..1..0..1. .2..1..2..1. .0..1..2..1
%e A274803 ..2..0..1..2. .1..0..1..0. .1..2..1..0. .0..2..1..0. .1..2..1..2
%Y A274803 Column 1 is A000079(n-2).
%Y A274803 Column 2 is A028859(n-1).
%K A274803 nonn,tabl
%O A274803 1,4
%A A274803 _R. H. Hardin_, Jul 07 2016