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 A229755 T(n,k)=Number of defective 4-colorings of an nXk 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order 8

%I

%S 0,0,0,1,3,1,3,60,60,3,12,422,598,422,12,50,1840,2347,2347,1840,50,

%T 210,6456,6809,6561,6809,6456,210,861,20032,17404,15075,15075,17404,

%U 20032,861,3416,57440,41872,32548,29776,32548,41872,57440,3416,13140,155904

%N T(n,k)=Number of defective 4-colorings of an nXk 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..3 order

%C Table starts

%C ...0.....0.....1......3.....12.....50....210....861....3416...13140...49230

%C ...0.....3....60....422...1840...6456..20032..57440..155904..406400.1027072

%C ...1....60...598...2347...6809..17404..41872..97565..223075..503650.1126490

%C ...3...422..2347...6561..15075..32548..69198.147376..315786..680124.1468934

%C ..12..1840..6809..15075..29776..57677.113330.228657..473562.1000381.2139866

%C ..50..6456.17404..32548..57677.102271.186396.354509..704530.1450667.3059672

%C .210.20032.41872..69198.113330.186396.314700.557578.1046550.2070144.4258696

%C .861.57440.97565.147376.228657.354509.557578.914039.1594164.2972289.5867806

%H R. H. Hardin, <a href="/A229755/b229755.txt">Table of n, a(n) for n = 1..575</a>

%F Empirical for column k:

%F k=1: a(n) = 12*a(n-1) -57*a(n-2) +136*a(n-3) -171*a(n-4) +108*a(n-5) -27*a(n-6) for n>9

%F k=2: a(n) = 6*a(n-1) -12*a(n-2) +8*a(n-3) for n>5

%F k=3: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>8

%F k=4: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11

%F k=5: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11

%F k=6: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11

%F k=7: a(n) = 9*a(n-1) -33*a(n-2) +63*a(n-3) -66*a(n-4) +36*a(n-5) -8*a(n-6) for n>11

%e Some solutions for n=4 k=4

%e ..0..1..2..0....0..1..2..1....0..1..2..1....0..1..2..1....0..1..0..1

%e ..0..3..2..3....3..3..0..3....2..3..0..3....3..2..0..3....2..2..3..2

%e ..2..1..0..1....2..1..2..2....3..1..2..1....1..2..1..2....3..0..0..1

%e ..0..3..2..3....0..3..0..1....2..3..0..3....0..3..0..3....1..2..3..2

%Y Column 1 is A229665

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_ Sep 28 2013

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Last modified September 19 17:32 EDT 2020. Contains 337178 sequences. (Running on oeis4.)