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A276299 T(n,k)=Number of nXk 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2. 13
1, 1, 2, 2, 4, 5, 4, 12, 11, 14, 8, 36, 45, 31, 41, 16, 108, 173, 189, 88, 122, 32, 324, 693, 1017, 805, 250, 365, 64, 972, 2765, 5909, 5965, 3437, 710, 1094, 128, 2916, 11061, 33461, 50949, 34865, 14693, 2016, 3281, 256, 8748, 44237, 191289, 408105, 442001 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Table starts
....1.....1.......2........4..........8...........16............32
....2.....4......12.......36........108..........324...........972
....5....11......45......173........693.........2765.........11061
...14....31.....189.....1017.......5909........33461........191289
...41....88.....805.....5965......50949.......408105.......3363533
..122...250....3437....34865.....442001......4988145......59728757
..365...710...14693...203933....3861469.....61239977....1073114625
.1094..2016...62829..1192701...33851605....752660245...19398127957
.3281..5724..268677..6974781..297360321...9254592049..352134188049
.9842.16252.1148973.40786925.2615328377.113817204341.6411366745009
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-3) for n>4
k=3: a(n) = 6*a(n-1) -8*a(n-2) +4*a(n-3) -7*a(n-4) +6*a(n-5) for n>7
k=4: [order 11] for n>13
k=5: [order 33] for n>37
k=6: [order 70] for n>75
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>2
n=3: a(n) = 4*a(n-1) +a(n-2) -4*a(n-3) for n>4
n=4: a(n) = 4*a(n-1) +10*a(n-2) -6*a(n-4) -22*a(n-5) +15*a(n-6) for n>8
n=5: [order 15] for n>17
n=6: [order 30] for n>32
n=7: [order 59] for n>61
EXAMPLE
Some solutions for n=4 k=4
..0..1..0..2. .0..1..2..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
..0..1..0..1. .2..1..2..1. .0..1..2..1. .0..1..0..1. .0..1..0..2
..0..2..0..1. .2..1..2..0. .2..1..0..1. .2..1..2..1. .0..2..0..2
..0..1..0..2. .0..1..2..0. .0..1..2..0. .0..1..0..1. .1..2..0..1
CROSSREFS
Column 1 is A007051(n-1).
Row 1 is A000079(n-2).
Row 2 is A003946(n-1).
Sequence in context: A252938 A229402 A266249 * A231302 A231363 A225840
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Aug 28 2016
STATUS
approved

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Last modified April 22 05:00 EDT 2024. Contains 371887 sequences. (Running on oeis4.)