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Search: id:A106376
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| A106376 |
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Number of binary trees (each vertex has 0, or 1 left, or 1 right, or 2 children) with n edges and having all leaves at the same level. |
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+0
2
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| 2, 5, 10, 24, 52, 121, 258, 616, 1344, 3128, 6996, 16160, 36248, 85041, 191298, 444168, 1019328, 2359392, 5405488, 12625336, 29066304, 67659824, 156911364, 365683744, 849401072, 1987046192, 4624252776, 10816019328
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Column sums of A106375.
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FORMULA
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See the Maple program where a recurrence relation for the triangle A106375(n, k) is given; A106376(k) is the sum of the terms in column k of this triangle.
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EXAMPLE
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a(3)=10 because we have eight paths of length 3 (each edge can have two orientations) and two trees in the shape of the letter Y (the bottom edge can have two orientations).
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MAPLE
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a:=proc(n, k) if n=1 and k=1 then 2 elif n=1 and k=2 then 1 elif n=1 then 0 elif k=1 then 0 else 2*a(n-1, k-1) + add(a(n-1, j)*a(n-1, k-2-j), j=1..k-3) fi end: seq(add(a(n, k), n=1..k), k=1..15); # a(n, k)=A106375(n, k)
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CROSSREFS
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Cf. A106375.
Sequence in context: A026754 A032170 A084081 this_sequence A151514 A001431 A054866
Adjacent sequences: A106373 A106374 A106375 this_sequence A106377 A106378 A106379
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 05 2005
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