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A115195
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Triangle of numbers, called Y(1,2), related to generalized Catalan numbers A062992(n) = C(2;n+1) = A064062(n+1).
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7
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1, 2, 3, 4, 10, 13, 8, 28, 54, 67, 16, 72, 180, 314, 381, 32, 176, 536, 1164, 1926, 2307, 64, 416, 1488, 3816, 7668, 12282, 14589, 128, 960, 3936, 11568, 26904, 51468, 80646, 95235, 256, 2176, 10048, 33184, 86992, 189928, 351220, 541690, 636925, 512, 4864
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OFFSET
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0,2
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COMMENTS
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This triangle Y(1,2) appears in the totally asymmetric exclusion process for the (unphysical) values alpha=1, beta=2. See the Derrida et al. refs. 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(2,n+1):=A064062(n+1).
The diagonal sequences give A064062(n+1), 2*A084076, 4*A115194, 8*A115202, 16*A115203, 32*A115204 for n+1>= M=1,..,6.
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LINKS
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Table of n, a(n) for n=0..46.
B. Derrida, E. Domany and D. Mukamel, An exact solution of a one-dimensional asymmetric exclusion model with open boundaries, J. Stat. Phys. 69, 1992, 667-687; eqs. (20), (21), p. 672.
Wolfdieter Lang, First 10 rows.
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FORMULA
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G.f. m-th diagonal, m>=1: ((1 + 2*x*c(2*x))*(2*x*c(2*x))^m)/(2*x*(1+x)) with c(x) the o.g.f. of A000108 (Catalan).
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EXAMPLE
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Triangle begins:
1;
2, 3;
4, 10, 13;
8, 28, 54, 67;
16, 72, 180, 314, 381;
...
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CROSSREFS
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Row sums give A084076.
Sequence in context: A250112 A193775 A131120 * A095384 A177084 A115899
Adjacent sequences: A115192 A115193 A115194 * A115196 A115197 A115198
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KEYWORD
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nonn,easy,tabl,changed
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AUTHOR
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Wolfdieter Lang, Feb 23 2006
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STATUS
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approved
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