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 A229586 T(n,k) = number of defective 3-colorings of an n X k 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order. 14
 0, 1, 0, 2, 6, 0, 6, 28, 40, 0, 16, 116, 264, 224, 0, 40, 444, 1620, 2160, 1152, 0, 96, 1620, 9156, 19764, 16416, 5632, 0, 224, 5724, 49848, 167364, 224532, 119232, 26624, 0, 512, 19764, 264300, 1375152, 2865780, 2440692, 839808, 122880, 0, 1152, 67068, 1374048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Table starts .0......1.......2.........6..........16...........40.............96 .0......6......28.......116.........444.........1620...........5724 .0.....40.....264......1620........9156........49848.........264300 .0....224....2160.....19764......167364......1375152.......11035044 .0...1152...16416....224532.....2865780.....35690460......435326724 .0...5632..119232...2440692....47091780....890824020....16551428868 .0..26624..839808..25745364...752194836..21639043284...613195191972 .0.122880.5785344.265720500.11768185764.515235810840.22285439501940 LINKS R. H. Hardin, Table of n, a(n) for n = 1..287 FORMULA Empirical for column k: k=1: a(n) = a(n-1). k=2: a(n) = 8*a(n-1) - 16*a(n-2) for n > 3. k=3: a(n) = 12*a(n-1) - 36*a(n-2). k=4: a(n) = 18*a(n-1) - 81*a(n-2) for n > 3. k=5: a(n) = 30*a(n-1) - 261*a(n-2) + 540*a(n-3) - 324*a(n-4). k=6: a(n) = 50*a(n-1) - 805*a(n-2) + 4662*a(n-3) - 12150*a(n-4) + 14580*a(n-5) - 6561*a(n-6). k=7: [order 8] Empirical for row n: n=1: a(n) = 4*a(n-1) - 4*a(n-2) for n > 4. n=2: a(n) = 6*a(n-1) - 9*a(n-2) for n > 4. n=3: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4) for n > 6. n=4: [order 6] for n > 12. n=5: [order 14] for n > 18. n=6: [order 18] for n > 26. n=7: [order 54] for n > 60. EXAMPLE Some solutions for n=3, k=4: 0 1 2 1 0 0 1 2 0 1 2 0 0 1 0 1 0 1 2 0 0 1 2 0 1 2 0 2 0 2 1 2 0 2 0 0 0 0 2 0 1 0 2 0 0 2 0 1 1 2 1 0 0 1 2 0 2 0 2 0 CROSSREFS Row 1 is A057711(n-1). Sequence in context: A345208 A241810 A156991 * A294789 A197035 A227805 Adjacent sequences: A229583 A229584 A229585 * A229587 A229588 A229589 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Sep 26 2013 STATUS approved

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Last modified March 27 20:39 EDT 2023. Contains 361575 sequences. (Running on oeis4.)