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A132887
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Number of symmetric paths in the first quadrant, from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0).
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0
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1, 1, 3, 2, 8, 6, 23, 17, 68, 51, 205, 154, 627, 473, 1937, 1464, 6032, 4568, 18900, 14332, 59519, 45187, 188211, 143024, 597241, 454217, 1900821, 1446604, 6065180, 4618576, 19396027
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(2n+1)=A059398(n); a(2n)=A059398(n-1)+A059398(n). The number of all paths in the first quadrant, from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0) is A128720(n).
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FORMULA
| G.f.=2(1+z+z^2)/[1-3z^2-z^4+sqrt((1+z^2-z^4)(1-3z^2-z^4))].
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EXAMPLE
| a(4)=8 because we have hhhh, hHh, HH, hUDh, UDUD, UhhD, UHD and UUDD.
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MAPLE
| G:=(2*(1+z+z^2))/(1-3*z^2-z^4+sqrt((1+z^2-z^4)*(1-3*z^2-z^4))): Gser:=series(G, z=0, 35): seq(coeff(Gser, z, n), n=0..30);
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CROSSREFS
| Cf. A128720, A059398.
Sequence in context: A122297 A073283 A117822 * A092174 A083514 A123696
Adjacent sequences: A132884 A132885 A132886 * A132888 A132889 A132890
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 05 2007
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