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A086115
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Number of 5 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing.
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4
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10, 100, 390, 1080, 2470, 4980, 9170, 15760, 25650, 39940, 59950, 87240, 123630, 171220, 232410, 309920, 406810, 526500, 672790, 849880, 1062390, 1315380, 1614370, 1965360, 2374850, 2849860, 3397950, 4027240, 4746430, 5564820
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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LINKS
| Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March challenge
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FORMULA
| a(n) = 1/6*n*(n^4+10*n^3+35*n^2+50*n-36). More generally, number of m X n (0, 1) matrices such that each row and each column is increasing or decreasing is 2*n*(2*binomial(n+m-1, n)-m) = 4/Beta(m, n)-2*m*n.
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CROSSREFS
| Cf. A032260, A016742, A086113, A086114.
Sequence in context: A095920 A134556 A060522 * A111434 A092707 A136876
Adjacent sequences: A086112 A086113 A086114 * A086116 A086117 A086118
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KEYWORD
| nonn
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AUTHOR
| Vladimir Baltic, Vladeta Jovovic (vladeta(AT)eunet.rs), Jul 10 2003
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