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A253449
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Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
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2
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81, 414, 1388, 3639, 8501, 19701, 48293, 126357, 346997, 982677, 2837237, 8295957, 24462197, 72541077, 215938037, 644449557, 1926625397, 5766435477, 17272430837, 51763547157, 155183156597, 465334505877, 1395573595637, 4185860948757
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OFFSET
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1,1
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COMMENTS
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Column 1 of A253456.
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LINKS
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R. H. Hardin, Table of n, a(n) for n = 1..210
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FORMULA
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Empirical: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) for n>10.
Empirical: a(n) = 400*3^(n-3) + 205*2^(n-1) + 2917 for n>7.
Empirical g.f.: x*(81 - 72*x - 205*x^2 - 621*x^3 - 549*x^4 + 396*x^5 + 1764*x^6 + 2304*x^7 + 1872*x^8 + 864*x^9) / ((1 - x)*(1 - 2*x)*(1 - 3*x)). - Colin Barker, Mar 20 2018
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EXAMPLE
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Some solutions for n=4:
..0..2....0..0....0..2....0..1....2..2....0..1....2..2....1..2....1..1....0..2
..1..2....1..1....0..1....1..1....0..0....0..0....0..0....2..2....2..0....2..1
..1..1....2..2....2..2....2..2....1..1....1..0....1..1....2..1....1..0....2..0
..1..0....0..0....1..2....2..2....0..0....2..1....2..2....1..1....2..2....2..1
..1..0....0..2....0..2....1..2....0..0....2..2....1..2....0..2....0..2....0..0
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CROSSREFS
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Cf. A253456.
Sequence in context: A253495 A253456 A236155 * A236148 A205986 A206668
Adjacent sequences: A253446 A253447 A253448 * A253450 A253451 A253452
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KEYWORD
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nonn
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AUTHOR
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R. H. Hardin, Jan 01 2015
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STATUS
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approved
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