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Search: id:A109980
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| A109980 |
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Number of Delannoy paths of length n with no (1,1)-steps on the line y=x (a Delannoy path of length n is a path from (0,0) to (n,n), consisting of steps E=(1,0), N=(0,1) and D=(1,1)). |
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+0
5
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| 1, 2, 8, 36, 172, 852, 4324, 22332, 116876, 618084, 3296308, 17702412, 95627580, 519170004, 2830862532, 15494401116, 85091200620, 468692890308, 2588521289812, 14330490031020, 79509491551772, 442019710668852
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equals left border of triangle A152250 and INVERTi transform of A001850, the Delannoy numbers: (1, 3, 13, 63, 321,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 30 2008]
Hankel transform is A036442. First column of Riordan array ((1-x)/(1+x), x/(1+3x+2x^2))^{-1}. [From Paul Barry (pbarry(AT)wit.ie), Apr 27 2009]
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REFERENCES
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R. A. Sulanke, Objects counted by the central Delannoy numbers, J. of Integer Sequences, 6, 2003, Article 03.1.5.
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FORMULA
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G.f.=1/[z+sqrt(1-6z+z^2)].
Moment representation: a(n)=(1/pi)int(x^n*sqrt(-x^2+6x-1)/(x(6-x)),x,3-2*sqrt(2),3+2*sqrt(2))+0^n/3. [From Paul Barry (pbarry(AT)wit.ie), Apr 27 2009]
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EXAMPLE
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a(2)=8 because we have NDE, EDN, NENE, NEEN, ENNE, ENEN, NNEE and EENN.
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MAPLE
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g:=1/(z+sqrt(1-6*z+z^2)): gser:=series(g, z=0, 28): 1, seq(coeff(gser, z^n), n=1..25);
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CROSSREFS
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First column of A109979.
A152250 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 30 2008]
Sequence in context: A147722 A089387 A084868 this_sequence A110837 A166229 A109318
Adjacent sequences: A109977 A109978 A109979 this_sequence A109981 A109982 A109983
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 06 2005
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