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Search: id:A025237
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| A025237 |
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G.f.: (1-x-sqrt(1-2*x-11*x^2))/(6*x^2). |
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+0
2
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| 1, 1, 4, 10, 37, 121, 451, 1639, 6259, 23923, 93502, 367852, 1465003, 5874103, 23740276, 96503554, 394542379, 1620716251, 6687296308, 27700303510, 115152607831, 480244735171, 2008802728819, 8425318166635, 35425680021397, 149296062114181, 630526903497706, 2668194946794124, 11311786743536125
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = (1/3)*s(n+2), where s = A014432.
Also, number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, 1), (1, 1)} - Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
Also, number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (-1, 1, 1), (0, 0, -1), (1, 1, 0)} - Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
Reversion of x/(1+x+3x^2). Hankel transform is 3^C(n+1,2) [A047656(n+1)]. [From Paul Barry (pbarry(AT)wit.ie), Sep 07 2009]
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LINKS
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A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
M. Bouquet-Melou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.
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FORMULA
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Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 07 2009: (Start)
G.f.: 1/(1-x-3x^2/(1-x-3x^2/(1-x-3x^2/(1-... (continued fraction);
a(n)=sum{k=0..floor(n/2), C(n,2k)*3^k*A000108(k)}. (End)
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PROGRAM
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(PARI) a(n)=polcoeff((1-x-6*x^2-sqrt(1-2*x-11*x^2+x^3*O(x^n)))/6, n+2) (from Michael Somos) [Produces sequence with a different offset]
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CROSSREFS
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Sequence in context: A052572 A079725 A154152 this_sequence A149188 A149189 A149190
Adjacent sequences: A025234 A025235 A025236 this_sequence A025238 A025239 A025240
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2008
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