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Search: id:A127525
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| A127525 |
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Number of ordered rooted trees where each subtree from given node has the same number of nodes. |
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+0
2
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| 1, 1, 2, 3, 5, 6, 12, 13, 24, 33, 60, 61, 142, 143, 289, 447, 699, 700, 1558, 1559, 3518, 5375, 8977, 8978, 17179, 20305, 40471, 54808, 98182, 98183, 242068, 242069, 477002, 695051, 1183654, 1510612, 2629806, 2629807, 5057173, 7928654, 12366025
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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a(1) = 1; a(n+1) = sum_{d|n} a(n/d)^d.
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EXAMPLE
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The tree shown below left counts, because the left subtree has 3 nodes, and so does the right subtree, and a similar condition holds for the subtrees. The tree shown on the right is not counted, because the left subtree has 3 nodes, while the right subtree has 4.
O..........O...O...O
|..........|....\./.
O...O...O..O.....O..
.\...\./....\....|..
.O...O......O...O..
..\./........\./...
...O..........O....
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CROSSREFS
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Cf. A000108, A127524, A007059.
Sequence in context: A112598 A078913 A114339 this_sequence A128958 A007435 A125877
Adjacent sequences: A127522 A127523 A127524 this_sequence A127526 A127527 A127528
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KEYWORD
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nonn
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AUTHOR
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Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jan 17 2007
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