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A215182
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T(n,k)=Number of nXnXn triangular 0..k arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value
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12
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2, 3, 2, 4, 4, 2, 5, 6, 5, 2, 6, 9, 12, 9, 2, 7, 12, 22, 26, 17, 2, 8, 16, 38, 83, 80, 48, 2, 9, 20, 64, 192, 412, 328, 141, 2, 10, 25, 98, 445, 1558, 3216, 1584, 559, 2, 11, 30, 145, 892, 5096, 18940, 36645, 9026, 2231, 2, 12, 36, 210, 1752, 14826, 102958, 364970, 635051
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OFFSET
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1,1
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COMMENTS
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Table starts
.2..3..4...5....6....7.....8.....9....10.....11.....12.....13......14......15
.2..4..6...9...12...16....20....25....30.....36.....42.....49......56......64
.2..5.12..22...38...64....98...145...210....291....394....526.....684.....876
.2..9.26..83..192..445...892..1752..3136...5494...9074..14716...22842...34868
.2.17.80.412.1558.5096.14826.39630.97184.223612.482160.991120.1946560.3679402
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LINKS
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FORMULA
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Empirical for row n:
n=1: a(k)=2*a(k-1)-a(k-2)
n=2: a(k)=2*a(k-1)-2*a(k-3)+a(k-4)
n=3: a(k)=2*a(k-1)-3*a(k-4)+3*a(k-6)-2*a(k-9)+a(k-10)
n=4: (order 39 symmetric)
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EXAMPLE
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Some solutions for n=4 k=4
.....3........2........1........3........2........3........3........2
....2.4......1.3......0.2......2.4......1.3......2.4......3.3......2.2
...2.3.4....1.2.3....0.1.2....1.4.4....1.1.4....2.3.4....2.3.4....2.2.2
..1.3.4.4..0.2.2.4..0.0.1.3..1.3.4.4..0.2.2.4..2.2.4.4..2.2.4.4..0.2.2.4
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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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