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A246747
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The number of binary heaps on n elements whose breadth-first search reading word avoids 231.
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2
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1, 1, 1, 2, 3, 7, 14, 37, 80, 222, 544, 1601, 4095, 12416, 33785, 105769, 293747, 935184, 2717376, 8848014, 26134254, 86210716, 262068267, 877833206, 2695238060, 9109101156, 28619396967, 97879220771, 310021153392, 1067906857449, 3440140082033, 11957123227292
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OFFSET
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0,4
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COMMENTS
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Also, the number of binary heaps on n elements whose breadth-first search reading word avoids 312.
Note that a breadth-first search reading word is equivalent to reading the tree labels left to right by levels, starting with the root.
For more information on heaps, see A056971.
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LINKS
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FORMULA
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a(n) = Sum_{i=0..floor((n-1)/2))} A000108(i)*a(n-i-1).
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EXAMPLE
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A heap on 4 elements is pictured in the 2nd link, and has breadth first reading word abcd. Then for n = 4 the a(4) = 3 heaps have reading words 1234, 1243, and 1324.
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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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