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Search: id:A127524
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| A127524 |
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Number of unordered 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, 11, 12, 20, 25, 42, 43, 81, 82, 150, 192, 287, 288, 563, 564, 982, 1277, 2182, 2183, 3658, 3785, 7108, 8659, 13101, 13102, 27827, 27828, 47768, 61025, 102355, 105689, 170882, 170883, 329651, 421547, 606283, 606284, 1193038
(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} C(a(n/d) + d-1, d).
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EXAMPLE
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The tree shown below left counts, because the subtree shown on the left has 3 nodes and so does the one on the right and a similar condition holds for the subtrees. The tree shown on the right is not counted, because the subtree shown on the left has 3 nodes, while the one on the right 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. A000081, A127525.
Sequence in context: A164523 A033159 A083710 this_sequence A117086 A081026 A137808
Adjacent sequences: A127521 A127522 A127523 this_sequence A127525 A127526 A127527
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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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