|
| |
|
|
A166135
|
|
Number of possible paths to each node that lies along the edge of a cut 4-nomial tree, that is rooted one unit from the cut.
|
|
0
| |
|
|
1, 1, 3, 7, 22, 65, 213, 693, 2352, 8034, 28014, 98505, 350548, 1256827, 4542395, 16517631, 60417708, 222087320, 820099720, 3040555978, 11314532376, 42243332130, 158196980682, 594075563613, 2236627194858, 8440468925400
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| This is the third member of an infinite series of infinite series, the first two being the Catalan and Motzkin integers. The Catalan numbers lie on the edge of cut 2-nomial trees, Motzkin integers on the edge of cut 3-nomial trees.
|
|
|
LINKS
| Illustration of 4-nomial graph The series is the one at the top.
First 4096 terms of the series in a text file.
Illustrates the sequence in context.The above reference gives the first 16 terms of the first 128 sequences in the family, of which this sequence is the third, the first being the Catalan numbers, the second the Motzkin integers, the fourth A104632.
|
|
|
FORMULA
| a(n) = ((36*n+18)*A092765(n)+(11*n+9)*A092765(n+1))/(2*(5*n+3)*(2*n+3)) (based on guessed recurrence) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 14 2010]
|
|
|
MAPLE
| This is a command line utility that generates the first 4096 terms of the sequence, compiled for OS X: http://www.jarosh.net/psi/Psi(4, 1).dmg
|
|
|
CROSSREFS
| A055113 is the third sequence from the top of the graph illustrated above. A126120, A000108, A001006.
Sequence in context: A079120 A092566 A036719 * A007595 A148681 A148682
Adjacent sequences: A166132 A166133 A166134 * A166136 A166137 A166138
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Rick Jarosh (rick(AT)jarosh.net), Oct 08 2009
|
| |
|
|
