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Search: id:A025243
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| A025243 |
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4. |
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+0
2
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| 1, 2, 1, 1, 3, 6, 14, 33, 79, 194, 482, 1214, 3090, 7936, 20544, 53545, 140399, 370098, 980226, 2607242, 6961462, 18652112, 50133616, 135140598, 365254226, 989614976, 2687312752, 7312725944, 19938170096, 54460115308, 149007155356, 408341969073
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = number of Dyck (n-1)-paths that contain no DUDUs and no UUDDs (n>=3). For example, a(5)=3 counts UUUDUDDD, UDUUDUDD, UUDUDDUD. - David Callan (callan(AT)stat.wisc.edu), Sep 25 2006
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FORMULA
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G.f.: (1+x+2*x^2-sqrt(1-2*x-3*x^2+4*x^4))/2 - Michael Somos, Jun 08, 2000.
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PROGRAM
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(PARI) a(n)=polcoeff((x+2*x^2-sqrt(1-2*x-3*x^2+4*x^4+x*O(x^n)))/2, n)
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CROSSREFS
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Sequence in context: A060517 A163181 A074662 this_sequence A144512 A159314 A135701
Adjacent sequences: A025240 A025241 A025242 this_sequence A025244 A025245 A025246
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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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