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%I #10 Apr 08 2021 07:25:15
%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 20032,861,3416,57440,41872,32548,29776,32548,41872,57440,3416,13140,155904,97565,69198,57677,57677,69198,97565,155904,13140
%N T(n,k) = number of defective 4-colorings of an n X k 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
%C 0 3 60 422 1840 6456 20032 57440 155904 406400
%C 1 60 598 2347 6809 17404 41872 97565 223075 503650
%C 3 422 2347 6561 15075 32548 69198 147376 315786 680124
%C 12 1840 6809 15075 29776 57677 113330 228657 473562 1000381
%C 50 6456 17404 32548 57677 102271 186396 354509 704530 1450667
%C 210 20032 41872 69198 113330 186396 314700 557578 1046550 2070144
%C 861 57440 97565 147376 228657 354509 557578 914039 1594164 2972289
%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