|
|
A048159
|
|
Triangle giving a(n,k) = number of (n,k) labeled Greg trees (n >= 2, 0 <= k <= n-2).
|
|
9
|
|
|
1, 3, 1, 16, 13, 3, 125, 171, 85, 15, 1296, 2551, 2005, 735, 105, 16807, 43653, 47586, 26950, 7875, 945, 262144, 850809, 1195383, 924238, 412650, 100485, 10395, 4782969, 18689527, 32291463, 31818045, 19235755, 7113645, 1486485, 135135
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,2
|
|
COMMENTS
|
An (n,k) Greg tree can be described as a tree with n black nodes and k white nodes where only the black nodes are labeled and the white nodes are of degree at least 3.
|
|
LINKS
|
|
|
FORMULA
|
a(n, 0) = n^(n-2), a(n, k) = (n+k-3)*a(n-1, k-1) + (2n+2k-3)*a(n-1, k) + (k+1)*a(n-1, k+1).
|
|
EXAMPLE
|
Triangle begins
1;
3, 1;
16, 13, 3;
125, 171, 85, 15;
...
|
|
MATHEMATICA
|
a[n_, 0] := n^(n-2); a[n_ /; n >= 2, k_] /; 0 <= k <= n-2 := a[n, k] = (n+k-3)*a[n-1, k-1] + (2*n+2*k-3)*a[n-1, k] + (k+1)*a[n-1, k+1]; a[n_, k_] = 0; Table[a[n, k], {n, 2, 9}, {k, 0, n-2}] // Flatten (* Jean-François Alcover, Oct 03 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
More terms from Larry Reeves (larryr(AT)acm.org), Apr 07 2000
|
|
STATUS
|
approved
|
|
|
|