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A059019
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Number of Dyck paths of semilength n with no peak at height 3.
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3
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1, 1, 2, 4, 9, 22, 58, 163, 483, 1494, 4783, 15740, 52956, 181391, 630533, 2218761, 7888266, 28291588, 102237141, 371884771, 1360527143, 5002837936, 18479695171, 68539149518, 255137783916, 952914971191, 3569834343547, 13410481705795
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Peart and Woan, in press, G_3(x).
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LINKS
| Guo-Niu Han, Enumeration of Standard Puzzles
P. Peart and W.-J. Woan, Dyck Paths With No Peaks at Height k, J. Integer Sequences, 4 (2001), #01.1.3.
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FORMULA
| G.f.: 2/(2-3*x+x*(1-4*x)^(1/2)).
a(n) = the upper left term in M^n, M = an infinite square production matrix in which a column of (1,1,0,0,0,...) is prepended to an infinite lower triangular matrix of all 1's and the rest zeros; as follows:
1, 1, 0, 0, 0, 0,...
1, 1, 1, 0, 0, 0,...
0, 1, 1, 1, 0, 0,...
0, 1, 1, 1, 1, 0,...
0, 1, 1, 1, 1, 1,...
...
- Gary W. Adamson, Jul 11 2011
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EXAMPLE
| 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 22*x^5 + 58*x^6 + ...
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CROSSREFS
| G_1, G_2, G_3, G_4 give A000957, A000108, A059019, A059027 resp.
Sequence in context: A124380 A176084 A192576 * A121953 A024427 A171367
Adjacent sequences: A059016 A059017 A059018 * A059020 A059021 A059022
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Feb 12 2001
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