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Permutations Number of permutations of [n] avoiding {4312, 1432, 1234}.
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Colin Barker, <a href="/A294766/b294766.txt">Table of n, a(n) for n = 0..1000</a>
<a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (13,-74,242,-501,681,-608,344,-112,16).
G.f.: (1 - 12*x + 63*x^2 - 188*x^3 + 350*x^4 - 419*x^5 + 317*x^6 - 138*x^7 + 26*x^8 - x^9) / ((1 - x)^5*(1 - 2*x)^4).
From Colin Barker, Nov 09 2017: (Start)
a(n) = (1/96)*(-6*(-16+2^n) + (-136+123*2^n)*n - 4*(11+3*2^(1+n))*n^2 + (-8+3*2^n)*n^3 - 4*n^4).
a(n) = 13*a(n-1) - 74*a(n-2) + 242*a(n-3) - 501*a(n-4) + 681*a(n-5) - 608*a(n-6) + 344*a(n-7) - 112*a(n-8) + 16*a(n-9) for n>9.
(End)
(PARI) Vec((1 - 12*x + 63*x^2 - 188*x^3 + 350*x^4 - 419*x^5 + 317*x^6 - 138*x^7 + 26*x^8 - x^9) / ((1 - x)^5*(1 - 2*x)^4) + O(x^30)) \\ Colin Barker, Nov 09 2017
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1, 1, 2, 6, 21, 74, 248, 784, 2355, 6785, 18897, 51177, 135358, 350788, 893038, 2237998, 5530485, 13496371, 32566359, 77785039, 184083080, 432004206, 1006097772, 2326777196, 5346673751, 12213795349, 27749494413, 62729986469, 141146690370, 316216935240, 705582559642, 1568468327962, 3474360060073, 7670811537703, 16883516381043, 37052682795883, 81093277441260, 177021371988946, 385481904658424
allocated for R. J. Mathar
Permutations of [n] avoiding {4312, 1432, 1234}.
1, 1, 2, 6, 21, 74, 248, 784, 2355, 6785, 18897, 51177, 135358, 350788, 893038, 2237998, 5530485, 13496371, 32566359, 77785039, 184083080, 432004206, 1006097772, 2326777196, 5346673751, 12213795349, 27749494413, 62729986469, 141146690370, 316216935240, 705582559642, 1568468327962, 3474360060073, 7670811537703, 16883516381043, 37052682795883, 81093277441260, 177021371988946, 385481904658424
0,3
D. Callan, T. Mansour, <a href="http://arxiv.org/abs/1705.00933">Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns</a>, arXiv:1705.00933 [math.CO] (2017), Table 2 No 119
(-350*x^4-63*x^2+419*x^5-26*x^8+138*x^7-317*x^6+188*x^3+x^9-1+12*x)/((2*x-1)^4*(x-1)^5) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;
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nonn,easy
R. J. Mathar, Nov 08 2017
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