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A339356
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Maximum number of copies of a 123456 permutation pattern in an alternating (or zig-zag) permutation of length n + 9.
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0
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16, 32, 144, 256, 688, 1120, 2352, 3584, 6496, 9408, 15456, 21504, 32928, 44352, 64416, 84480, 117744, 151008, 203632, 256256, 336336, 416416, 534352, 652288, 821184, 990080, 1226176, 1462272, 1785408, 2108544, 2542656, 2976768, 3550416, 4124064, 4870992, 5617920, 6577648
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OFFSET
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1,1
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COMMENTS
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The maximum number of copies of 123 in an alternating permutation is motivated in the Notices reference, and the argument here is analogous.
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LINKS
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FORMULA
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a(2n) = 32*A040977(n-1) = 64*C(n+5,6) - 32*C(n+4,5).
a(2n-1) = 16*A259181(n) = (2*n*(n + 1)*(n + 2)*(n + 3)*(2*n^2 + 6*n + 7))/45.
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EXAMPLE
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a(1) = 16. The alternating permutation of length 1+9=10 with the maximum number of copies of 123456 is 132547698(10). The sixteen copies are 12468(10), 12469(10), 12478(10), 12479(10), 12568(10), 12569(10), 12578(10), 12579(10), 13468(10), 13469(10), 13478(10), 13479(10), 13568(10), 13569(10), 13578(10), and 13579(10).
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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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