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Search: id:A059480
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| 1, 1, 4, 8, 28, 76, 272, 880, 3328, 12128, 48736, 194272, 827840, 3547648, 15965248, 72727616, 344136832, 1653233920, 8191833728, 41256512128, 213285020416, 1120928287232, 6026483756800, 32928762650368, 183590856570368
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,200
S. Kitaev and T. Mansour, On multi-avoidance of generalized patterns.
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FORMULA
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a(n) = a(n - 1) + (n + 1)*a(n - 2); a(0) = a(1) = 1; E.g.f. = ( - 2*(1 + x) + e^((x*(2 + x))/2)*(2 + x*(2 + x))*(2 + Sqrt[2*e*Pi]*erf[1/Sqrt[2]]) - e^((1 + x)^2/2)*Sqrt[2*Pi]*(2 + x*(2 + x))*Erf[(1 + x)/Sqrt[2]])/2
With offset 2: number of permutations that simultaneously avoid the patterns 12-3 and 21-3 and start with 1 and end with 12. E.g.f.: exp(x+x^2/2) * {1-int[0..x, exp(-t-t^2/2) dt]} - 1.
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PROGRAM
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(PARI) { a=b=c=1; for (n = 0, 200, if (n>1, a=b + (n + 1)*c; c=b; b=a); write("b059480.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 27 2009]
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CROSSREFS
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Sequence in context: A020138 A090083 A034515 this_sequence A105723 A143555 A025234
Adjacent sequences: A059477 A059478 A059479 this_sequence A059481 A059482 A059483
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KEYWORD
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nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Feb 15 2001
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