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A109078
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Number of symmetric Dyck paths of semilength n and having no hills (i.e. no peaks at level 1).
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1
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1, 0, 1, 2, 4, 6, 13, 22, 46, 80, 166, 296, 610, 1106, 2269, 4166, 8518, 15792, 32206, 60172, 122464, 230252, 467842, 884236, 1794196, 3406104, 6903352, 13154948, 26635774, 50922986, 103020253, 197519942, 399300166, 767502944, 1550554582
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Column 0 of A109077.
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FORMULA
| G.f.=2[1-z+2z^2+(1-z)q]/[1-2z+q)(1+2z^2+q)], where q=sqrt(1-4z^2).
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EXAMPLE
| a(4)=4 because we have uudduudd, uudududd, uuududdd and uuuudddd, where u=(1,1), d=(1,-1).
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MAPLE
| g:=2*(1-z-z*sqrt(1-4*z^2)+2*z^2+sqrt(1-4*z^2))/(1+sqrt(1-4*z^2)-2*z)/(1+sqrt(1-4*z^2)+2*z^2): gser:=series(g, z=0, 39): 1, seq(coeff(gser, z^n), n=1..36);
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CROSSREFS
| Cf. A109077.
Bisections are A026641 and A072547.
Sequence in context: A110980 A058598 A087549 * A033305 A105543 A027712
Adjacent sequences: A109075 A109076 A109077 * A109079 A109080 A109081
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 17 2005
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