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A111053
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Number of permutations which avoid the patterns 1324 and (2143 with Bruhat restriction {2<->3}). Also the number of permutations whose graphs are acyclic.
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0
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1, 2, 6, 22, 89, 379, 1661, 7405, 33367, 151398, 690147, 3156112, 14465746, 66409493, 305232025, 1404129530, 6463476538, 29767212095, 137142651679, 632021380433, 2913316615372, 13431328632593, 61931182541194, 285592218851606, 1317104663887309, 6074682489939359, 28018852961838675, 129239701278757210
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| S. Butler, On permutations which are 1324 and {overline 2143} avoiding.
M. Bousquet-Melou and S. Butler, Forest-like permutations
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FORMULA
| G.f.: ((1-X)*(1-4*X-2*X*X)-(1-5*X)*sqrt(1-4*X))/2/(1-5*X+2*X^2-X^3. - Ralf Stephan, May 09 2007
G.f.: 2 * x * (1 - 4*x - x^2) / ((1 - x) * (1 - 4*x - 2*x^2) + (1 - 5*x) * sqrt(1 - 4*x)). - Michael Somos, Jan 12 2012
G.f. is the power series composition of g.f. A204200 and g.f. A000108 (Catalan) with offset 1. - Michael Somos, Jan 12 2012
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EXAMPLE
| x + 2*x^2 + 6*x^3 + 22*x^4 + 89*x^5 + 379*x^6 + 1661*x^7 + 7405*x^8 + ...
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PROG
| (PARI) x='x+O('x^66); /* that many terms */
gf=((1-x)*(1-4*x-2*x^2)-(1-5*x)*sqrt(1-4*x))/(2*(1-5*x+2*x^2-x^3));
Vec(gf) /* show terms */ /* Joerg Arndt, Jun 25 2011 */
(PARI) {a(n) = if( n<0, 0, polcoeff( 2 * x * (1 - 4*x - x^2) / ((1 - x) * (1 - 4*x - 2*x^2) + (1 - 5*x) * sqrt(1 - 4*x + x * O(x^n))), n))} /* Michael Somos, Jan 12 2012 */
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CROSSREFS
| Cf. A204200.
Sequence in context: A165522 A150267 A165540 * A165541 A165542 A165543
Adjacent sequences: A111050 A111051 A111052 * A111054 A111055 A111056
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KEYWORD
| nonn
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AUTHOR
| Steven K. Butler (sbutler(AT)math.ucsd.edu), Oct 06 2005
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EXTENSIONS
| Added more terms, Joerg Arndt, Jun 25 2011.
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