|
| |
|
|
A144944
|
|
Super-Catalan triangle (read by rows) = triangular array associated with little Schroeder numbers (read by rows): T(0,0)=1, T(p,q)=T(p,q-1) if 0<p=q, T(p,q)=T(p,q-1)+T(p-1,q)+T(p-1,q-1) if -1<p<q and T(p,q)=0 otherwise.
|
|
4
|
|
|
|
1, 1, 1, 1, 3, 3, 1, 5, 11, 11, 1, 7, 23, 45, 45, 1, 9, 39, 107, 197, 197, 1, 11, 59, 205, 509, 903, 903, 1, 13, 83, 347, 1061, 2473, 4279, 4279, 1, 15, 111, 541, 1949, 5483, 12235, 20793, 20793, 1, 17, 143, 795, 3285, 10717, 28435, 61463, 103049, 103049
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
|
|
|
EXAMPLE
|
First few rows of the triangle:
1
1,1
1,3,3
1,5,11,11
1,7,23,45,45
1,9,39,107,197,197
1,11,59,205,509,903,903
|
|
|
MATHEMATICA
|
t[_, 0] = 1; t[p_, p_] := t[p, p] = t[p, p-1]; t[p_, q_] := t[p, q] = t[p, q-1] + t[p-1, q] + t[p-1, q-1]; Flatten[ Table[ t[p, q], {p, 0, 6}, {q, 0, p}]] (* From Jean-François Alcover, Dec 19 2011 *)
|
|
|
PROG
|
Haskell)
a144944 n k = a144944_tabl !! n !! k
a144944_row n = a144944_tabl !! n
a144944_tabl = iterate f [1] where
f us = vs ++ [last vs] where
vs = scanl1 (+) $ zipWith (+) us $ [0] ++ us
-- Reinhard Zumkeller, May 11 2013
|
|
|
CROSSREFS
|
Super-Catalan numbers or little Schroeder numbers (cf. A001003) appear on the diagonal.
Generalizes the Catalan triangle (A009766) and hence the ballot Numbers.
Cf. A033877 for a similar triangle derived from the large Schroeder numbers (A006318).
Cf. A010683 (row sums), A186826 (rows reversed).
Sequence in context: A193823 A071945 A209583 * A137426 A074456 A016454
Adjacent sequences: A144941 A144942 A144943 * A144945 A144946 A144947
|
|
|
KEYWORD
|
nice,nonn,tabl,changed
|
|
|
AUTHOR
|
Johannes Fischer (Fischer(AT)informatik.uni-tuebingen.de), Sep 26 2008
|
|
|
STATUS
|
approved
|
| |
|
|
