|
Search: id:A117357
|
|
|
| A117357 |
|
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 1). |
|
+0
5
|
|
| 0, 1, 0, 1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 7, 7, 11, 12, 16, 19, 25, 29, 38, 46, 59, 72, 91, 110, 141, 171, 214, 264, 331, 405, 509, 623, 777, 957, 1189, 1462, 1822, 2235, 2774, 3418, 4228, 5205, 6442, 7922, 9793, 12053, 14870
(list; graph; listen)
|
|
|
OFFSET
|
0,10
|
|
|
FORMULA
|
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).
|
|
EXAMPLE
|
a(9) = 2; there is one tree with root at height 1 and 4 nodes at height 2 (1+4*2 = 9), and one with root at height 1, 1 node at height 2, and 2 nodes at height 3 (1+2+2*3 = 9).
|
|
CROSSREFS
|
Cf. A117356, A000081.
Sequence in context: A017980 A064650 A130083 this_sequence A029020 A035380 A036823
Adjacent sequences: A117354 A117355 A117356 this_sequence A117358 A117359 A117360
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 09 2006
|
|
|
Search completed in 0.002 seconds
|
