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A215184
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Number of 4 X 4 X 4 triangular 0..n 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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1
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2, 9, 26, 83, 192, 445, 892, 1752, 3136, 5494, 9074, 14716, 22842, 34868, 51570, 75217, 106968, 150289, 207026, 282233, 378516, 503027, 659558, 857984, 1103346, 1408886, 1781610, 2238970, 2789894, 3457002, 4252128, 5204053, 6327530, 7658725, 9216516
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Empirical: a(n) = 2*a(n-1) -2*a(n-2) +3*a(n-3) -2*a(n-4) +2*a(n-6) -6*a(n-7) +9*a(n-8) -12*a(n-9) +10*a(n-10) -7*a(n-11) +3*a(n-12) +6*a(n-13) -12*a(n-14) +19*a(n-15) -21*a(n-16) +20*a(n-17) -14*a(n-18) +3*a(n-19) +3*a(n-20) -14*a(n-21) +20*a(n-22) -21*a(n-23) +19*a(n-24) -12*a(n-25) +6*a(n-26) +3*a(n-27) -7*a(n-28) +10*a(n-29) -12*a(n-30) +9*a(n-31) -6*a(n-32) +2*a(n-33) -2*a(n-35) +3*a(n-36) -2*a(n-37) +2*a(n-38) -a(n-39).
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EXAMPLE
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Some solutions for n=4
.....1........2........1........1........2........1........1........1
....1.1......1.3......0.2......1.1......1.3......1.1......0.2......1.1
...1.1.1....1.1.4....0.0.3....0.0.3....0.2.4....1.1.1....0.1.2....0.1.2
..1.1.1.1..0.2.2.4..0.0.1.3..0.0.1.3..0.0.4.4..0.1.1.2..0.0.2.2..0.0.2.2
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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