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Search: id:A025266
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| A025266 |
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a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4. |
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+0
2
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| 1, 1, 0, 1, 2, 6, 16, 45, 126, 358, 1024, 2954, 8580, 25084, 73760, 218045, 647670, 1932230, 5787520, 17398270, 52476700, 158765300, 481690080, 1465239250, 4467799212, 13653601116, 41812009216, 128290240180, 394338641416, 1214165174712
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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a(n+2)=number of Motzkin (2n)-paths whose longest plateau is of length n. A plateau is a sequence of contiguous flatsteps that is either the entire path or is of length >=1 and preceded by an up step and followed by a down step. Example: for n=3; a(5) counts UFFFDF and FUFFFD. - David Callan (callan(AT)stat.wisc.edu), Jul 15 2004
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FORMULA
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G.f.: (1-sqrt(1-4*x+8*x^3))/2 - Michael Somos, Jun 08, 2000.
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PROGRAM
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(PARI) a(n)=polcoeff((1-sqrt(1-4*x+8*x^3+x*O(x^n)))/2, n)
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CROSSREFS
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Cf. A025264.
Sequence in context: A126285 A026163 A005717 this_sequence A074403 A098617 A092687
Adjacent sequences: A025263 A025264 A025265 this_sequence A025267 A025268 A025269
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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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