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A270509
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T(n,k)=Number of nXnXn triangular 0..k arrays with some element plus some adjacent element totalling k+1 exactly once.
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13
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0, 0, 3, 0, 6, 15, 0, 21, 144, 126, 0, 36, 1137, 5406, 1149, 0, 63, 4584, 132474, 369072, 14220, 0, 90, 15843, 1522068, 34889103, 47829828, 230247, 0, 129, 40392, 12034134, 1489277664, 22383193638, 12072484260, 5038371, 0, 168, 95109, 65046258
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OFFSET
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1,3
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COMMENTS
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Table starts
......0...........0..............0.................0....................0
......3...........6.............21................36...................63
.....15.........144...........1137..............4584................15843
....126........5406.........132474...........1522068.............12034134
...1149......369072.......34889103........1489277664..........32485734273
..14220....47829828....22383193638.....4560833505432......332450685760224
.230247.12072484260.35714928884139.44967908021958960.13296639688401609639
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LINKS
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FORMULA
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Empirical for row n:
n=2: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
n=3: [order 10]
n=4: [order 18]
Empirical quasipolynomials for row n:
n=2: polynomial of degree 2 plus a quasipolynomial of degree 0 with period 2
n=3: polynomial of degree 5 plus a quasipolynomial of degree 3 with period 2
n=4: polynomial of degree 9 plus a quasipolynomial of degree 7 with period 2
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EXAMPLE
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Some solutions for n=3 k=4
....0......0......2......1......0......0......4......0......1......0......2
...2.3....4.0....0.1....1.0....3.3....3.2....3.0....3.2....0.2....2.4....1.2
..4.0.1..1.0.1..4.3.4..3.2.4..3.4.1..3.0.0..4.2.1..4.4.2..3.2.4..2.1.3..2.0.3
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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