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A165541
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Number of permutations of length n which avoid the patterns 4213 and 3142.
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0
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1, 2, 6, 22, 89, 379, 1664, 7460, 33977, 156727, 730619, 3436710, 16291842, 77758962, 373369867, 1802399037, 8742691627, 42590945206, 208300979739, 1022385319050, 5034470059883, 24865173540949, 123147075005750
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f. f satisfies: x^3*f^6+(7*x^3-7*x^2+2*x)*f^5+(x^4+14*x^3-21*x^2+10*x-1)*f^4+(4*x^4+8*x^3-19*x^2+11*x-2)*f^3+(6*x^4-5*x^3-2*x^2+2*x)*f^2+(4*x^4-7*x^3+4*x^2-x)*f+x^4-2*x^3+x^2 = 0.
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EXAMPLE
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There are 22 permutations of length 4 which avoid these two patterns, so a(4)=22.
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MATHEMATICA
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f = 0; m = 24;
Do[f = -(1/(x(4x^3 - 7x^2 + 4x - 1)))(x^3 f^6 + x(7x^2 - 7x + 2) f^5 + (x^4 + 14x^3 - 21x^2 + 10x - 1) f^4 + (1 - 2x)^2 (x^2 + 3x - 2) f^3 + x(6 x^3 - 5x^2 - 2x + 2) f^2 + (x-1)^2 x^2) + O[x]^m, {m}];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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