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A089324
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Number of lattice paths from (0,0) to the line x+y=n that use the step set {(0,1),(1,0),(2,0),(3,0),...} and never pass below y=x.
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2
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1, 1, 2, 3, 7, 12, 29, 53, 130, 247, 611, 1192, 2965, 5897, 14726, 29723, 74443, 152020, 381617, 786733, 1978582, 4111295, 10355303, 21661168, 54628201, 114925697, 290148890, 613442227, 1550177791, 3291704108, 8324934533, 17745496453
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n)=Sum(A011117(i,n-i),i=0..floor(n/2)), i.e. diagonal sums in A011117 formatted as an upper right triangle.
Hankel transform is A060656. [From Paul Barry (pbarry(AT)wit.ie), Mar 01 2010]
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FORMULA
| G.f.=2/[(1-z)^2+sqrt(1-6z^2+z^4)].
G.f.: 1/(1-x-x^2/(1-2x^2/(1-x^2/(1-2x^2/(1-x^2/(1-2x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Mar 01 2010]
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EXAMPLE
| a(4)=7 because we have VVVV, VVVh, VVhV, VhVV, VVH, VVhh and VhVh, where V=(0,1), h=(1,0) and H=(2,0).
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CROSSREFS
| Cf. A011117.
Sequence in context: A182692 A032173 A130616 * A111759 A047749 A134565
Adjacent sequences: A089321 A089322 A089323 * A089325 A089326 A089327
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 25 2003
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