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Search: id:A106050
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| 0, 0, 0, 1, 3, 13, 42, 146, 476, 1574, 5122, 16706, 54256, 176254, 571954, 1856245, 6023681, 19551939, 63476314, 206145075, 669695819, 2176401235, 7075521724, 23011145314, 74864599954, 243652588070, 793264765396, 2583532274289, 8416929889967, 27430452311513
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Number of paths in the right-half-plane from (0,0) to (n-1,2) consisting of steps U=(1,1), D=(1,-1), h=(1,0), and H=(2,0). Example: a(4)=3 because we have hUU, UhU, and UUh. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 03 2007
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LINKS
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W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.
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FORMULA
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G.f.=z^3*g^2/sqrt((1+z-z^2)(1-3z-z^2)), where g=1+zg+z^2*g+z^2*g^2=[1-z-z^2-sqrt((1+z-z^2)(1-3z--z^2))]/(2z^2). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 03 2007
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MAPLE
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g:=((1-z-z^2-sqrt((1+z-z^2)*(1-3*z-z^2)))*1/2)/z^2: gser:=series(z^3*g^2/sqrt((1+z-z^2)*(1-3*z-z^2)), z=0, 32): seq(coeff(gser, z, n), n=0..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 03 2007
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CROSSREFS
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Cf. A059317, A059345, A106053.
Adjacent sequences: A106047 A106048 A106049 this_sequence A106051 A106052 A106053
Sequence in context: A049167 A121162 A109224 this_sequence A074425 A041499 A093923
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KEYWORD
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nonn
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AUTHOR
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njas, May 28 2005
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