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A116868
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Triangle of numbers, called Y(1,3), related to generalized Catalan numbers A064063(n)=:C(3;n).
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3
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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; internal format)
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OFFSET
| 0,2
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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).
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LINKS
| W. Lang: First 10 rows.
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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).
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EXAMPLE
| [1];[3,4];[9,21,25];[27,90,165,190];[81,351,846,1416,1606];...
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CROSSREFS
| Row sums give A116862.
Sequence in context: A110810 A049978 A092763 * A049976 A032789 A089243
Adjacent sequences: A116865 A116866 A116867 * A116869 A116870 A116871
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 24 2006
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