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A085362
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a(0)=1, for n>0: a(n)=2*5^(n-1)-(1/2)Sum a(i)a(n-i),(i=1,..,n-1).
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6
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1, 2, 8, 34, 150, 678, 3116, 14494, 68032, 321590, 1528776, 7301142, 35003238, 168359754, 812041860, 3926147730, 19022666310, 92338836390, 448968093320, 2186194166950, 10659569748370, 52037098259090, 254308709196660
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OFFSET
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0,2
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COMMENTS
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Number of bilateral Schroeder paths (i.e. lattice paths consisting of steps U=(1,1), D=(1,-1) and H=(2,0)) from (0,0) to (2n,0) and with no H-steps at even (zero, positive or negative) levels. Example: a(2)=8 because we have UDUD, UUDD, UHD, UDDU and their reflections in the x-axis. First differences of A026375. - Emeric Deutsch, Jan 28 2004
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
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FORMULA
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G.f.: sqrt((1-x)/(1-5*x))
5^n = sum(i=0..n, sum(j=0..i, a(j)*a(i-j) )).
a(n) = (2*(3*n-2)*a(n-1)-5*(n-2)*a(n-2)])n; a(0)=1, a(1)=2. - Emeric Deutsch, Jan 28 2004
a(n) ~ 2*5^(n-1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 14 2012
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MATHEMATICA
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CoefficientList[Series[Sqrt[(1-x)/(1-5x)], {x, 0, 25}], x]
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PROG
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(PARI) x='x+O('x^66); Vec(sqrt((1-x)/(1-5*x))) \\ Joerg Arndt, May 10 2013
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CROSSREFS
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Cf. A026375.
Bisection of A026392. Cf. A026375.
Cf. A026387. [From R. J. Mathar, Sep 12 2008]
Sequence in context: A067336 A151829 A026387 * A150889 A150890 A150891
Adjacent sequences: A085359 A085360 A085361 * A085363 A085364 A085365
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jun 25 2003
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STATUS
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approved
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