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Search: id:A117356
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| A117356 |
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Number of rooted trees with total weight n, where the weight of a node at height k is k (with the root considered to be at level 0). |
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+0
2
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| 1, 1, 1, 2, 2, 3, 5, 6, 8, 12, 16, 22, 31, 41, 56, 78, 104, 142, 194, 260, 353, 478, 641, 864, 1164, 1560, 2095, 2810, 3757, 5028, 6722, 8966, 11963, 15945, 21223, 28244, 37551, 49871, 66210, 87829, 116411, 154222, 204162, 270084, 357117, 471881, 623146
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OFFSET
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0,4
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COMMENT
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Equivalently, number of forests of total weight n, when the roots are considered to be at height 1; so this is the Euler transform of A117357. [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 03 2009]
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FORMULA
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If a<k>(n) is the equivalent of this sequence with the root node considered to be at level k, then a<k>(n) is the Euler transform of a<k+1>(n) shifted right k places. To compute N terms, take k so that (k+1)*(k+2)/2 > N, approximate a<k>(n) by 1 if n=k, 0 otherwise and apply this rule repeatedly. Formula from Christian G. Bower (bowerc(at)usa.net).
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EXAMPLE
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a(3) = 2; there is one tree with 3 nodes at height 1 and one with 1 node at height 1 and 1 at height 2.
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CROSSREFS
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Cf. A117357, A000081.
Sequence in context: A129838 A032153 A116465 this_sequence A017819 A050044 A143438
Adjacent sequences: A117353 A117354 A117355 this_sequence A117357 A117358 A117359
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KEYWORD
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nonn
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 09 2006
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