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 A275142 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2. 11
 1, 1, 2, 2, 6, 5, 4, 16, 36, 14, 8, 48, 80, 216, 41, 16, 144, 224, 400, 1296, 122, 32, 432, 528, 1088, 2000, 7776, 365, 64, 1296, 1216, 2320, 5248, 10000, 46656, 1094, 128, 3888, 2816, 6464, 9744, 25344, 50000, 279936, 3281, 256, 11664, 6544, 17872, 32384, 41360 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....1........1.......2........4........8........16........32.........64 ....2........6......16.......48......144.......432......1296.......3888 ....5.......36......80......224......528......1216......2816.......6544 ...14......216.....400.....1088.....2320......6464.....17872......49792 ...41.....1296....2000.....5248.....9744.....32384....107472.....362176 ..122.....7776...10000....25344....41360....165568....663904....2695808 ..365....46656...50000...122368...175120....841536...4055152...19906560 .1094...279936..250000...590848...741904...4283968..24875600..147762240 .3281..1679616.1250000..2852864..3142672..21800000.152379136.1093999424 .9842.10077696.6250000.13774848.13312656.110943552.933805200.8109111360 LINKS R. H. Hardin, Table of n, a(n) for n = 1..721 FORMULA Empirical for column k: k=1: a(n) = 4*a(n-1) -3*a(n-2) k=2: a(n) = 6*a(n-1) k=3: a(n) = 5*a(n-1) for n>2 k=4: a(n) = 4*a(n-1) +4*a(n-2) for n>3 k=5: a(n) = 3*a(n-1) +5*a(n-2) +a(n-3) for n>4 k=6: a(n) = 3*a(n-1) +10*a(n-2) +4*a(n-3) -4*a(n-4) for n>6 k=7: a(n) = 3*a(n-1) +18*a(n-2) +11*a(n-3) -23*a(n-4) -4*a(n-5) for n>7 Empirical for row n: n=1: a(n) = 2*a(n-1) for n>2 n=2: a(n) = 3*a(n-1) for n>3 n=3: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) for n>5 n=4: a(n) = 5*a(n-1) -9*a(n-2) +10*a(n-3) -6*a(n-4) +a(n-5) for n>9 n=5: [order 8] for n>12 n=6: [order 13] for n>18 n=7: [order 21] for n>27 EXAMPLE Some solutions for n=5 k=4 ..0..1..2..1. .0..1..0..1. .0..1..0..2. .0..1..2..1. .0..1..2..0 ..2..0..1..0. .0..2..1..2. .2..0..1..2. .2..0..2..0. .0..1..2..0 ..2..0..1..2. .1..2..1..0. .1..2..1..2. .2..0..1..2. .2..0..2..0 ..1..2..0..1. .0..1..2..1. .0..2..0..1. .2..0..1..2. .2..0..1..2 ..0..2..0..1. .2..1..2..0. .0..1..2..0. .1..2..0..2. .0..1..0..1 CROSSREFS Column 1 is A007051(n-1). Column 2 is A000400(n-1). Column 3 is A055842. Row 1 is A000079(n-2). Sequence in context: A181661 A144160 A368228 * A200226 A300628 A115255 Adjacent sequences: A275139 A275140 A275141 * A275143 A275144 A275145 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Jul 17 2016 STATUS approved

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Last modified April 22 10:51 EDT 2024. Contains 371897 sequences. (Running on oeis4.)