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A116868 Triangle of numbers, called Y(1,3), related to generalized Catalan numbers A064063(n)=:C(3;n). 3
1, 3, 4, 9, 21, 25, 27, 90, 165, 190, 81, 351, 846, 1416, 1606, 243, 1296, 3834, 8082, 12900, 14506, 729, 4617, 16119, 40365, 79065, 122583, 137089, 2187, 16038, 64395, 185490, 422685, 790434, 1201701, 1338790 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

This triangle Y(1,3) appears in the totally asymmetric exclusion process for the (unphysical) values alpha=1, beta=3. See the Derrida et al. reference given under A064094, where the triangle entries are called Y_{N,K} for given alpha and beta.

The main diagonal (M=1) gives the generalized Catalan sequence C(3;n+1):= A064063(n+1).

LINKS

Table of n, a(n) for n=0..35.

W. Lang: First 10 rows.

FORMULA

G.f. m-th diagonal, m>=1:((3*x*c(3*x))^m)*(2 + 3*x*c(3*x))/(3*x*(2+x))) with c(x) the o.g.f. of A000108 (Catalan).

EXAMPLE

[1];[3,4];[9,21,25];[27,90,165,190];[81,351,846,1416,1606];...

CROSSREFS

Row sums give A116862.

Sequence in context: A324764 A092763 A232955 * A049976 A032789 A089243

Adjacent sequences:  A116865 A116866 A116867 * A116869 A116870 A116871

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Mar 24 2006

STATUS

approved

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Last modified May 21 01:18 EDT 2019. Contains 323429 sequences. (Running on oeis4.)