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Search: id:A086114
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| A086114 |
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Number of 4 X n (0,1) matrices such that each row and each column is nondecreasing or nonincreasing. |
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+0
3
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| 8, 64, 216, 528, 1080, 1968, 3304, 5216, 7848, 11360, 15928, 21744, 29016, 37968, 48840, 61888, 77384, 95616, 116888, 141520, 169848, 202224, 239016, 280608, 327400, 379808, 438264, 503216, 575128, 654480, 741768, 837504, 942216, 1056448
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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Don Coppersmith, Ponder This: IBM Research Monthly Puzzles, March challenge
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FORMULA
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a(n) = 2/3*n*(n^3+6*n^2+11*n-6). 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
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Cf. A032260, A016742, A086113, A086115.
Adjacent sequences: A086111 A086112 A086113 this_sequence A086115 A086116 A086117
Sequence in context: A043152 A044195 A016743 this_sequence A117219 A045825 A122093
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic, Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 10 2003
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