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A137842
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Number of paths from (0,0) to (3n,0) that stay in first quadrant (but may touch horizontal axis) and where each step is (2,1), (1,2) or (1,-1).
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0
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1, 1, 2, 4, 10, 24, 66, 172, 498, 1360, 4066, 11444, 34970, 100520, 312066, 911068, 2862562, 8457504, 26824386, 80006116, 255680170, 768464312, 2471150402, 7474561164, 24161357010, 73473471344, 238552980386, 728745517972
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Row sums of the inverse of the Riordan array (1/(1+x^2),x(1-x^2)/(1+x^2)).
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FORMULA
| G.f.: (1+v^2)/(1-v), where v=2*sqrt(x^2+3)*sin(asin(x(x^2+18)/((x^2+3)^(3/2)))/3)/3-x/3; a(2n)=A027307(n); a(2n+1)=A032349(n+1).
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CROSSREFS
| Cf. A084078. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 28 2009]
Sequence in context: A049144 A049131 A084078 * A049146 A000682 A001997
Adjacent sequences: A137839 A137840 A137841 * A137843 A137844 A137845
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 13 2008
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