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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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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PROG
| (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
| Sequence in context: A060517 A163181 A074662 * A144512 A159314 A135701
Adjacent sequences: A025240 A025241 A025242 * A025244 A025245 A025246
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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