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A098992 Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324. 1

%I #6 Oct 26 2017 07:47:58

%S 0,0,1,11,55,190,526,1254,2682,5280,9735,17017,28457,45838,71500,

%T 108460,160548,232560,330429,461415,634315,859694,1150138,1520530,

%U 1988350,2574000,3301155,4197141,5293341,6625630,8234840,10167256,12475144,15217312,18459705

%N Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324.

%H Colin Barker, <a href="/A098992/b098992.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F G.f.: x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8.

%F From _Colin Barker_, Oct 26 2017: (Start)

%F a(n) = (n*(-540 + 476*n + 469*n^2 - 490*n^3 + 70*n^4 + 14*n^5 + n^6)) / 5040.

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.

%F (End)

%o (PARI) concat(vector(2), Vec(x^3*(1 + 3*x - 5*x^2 + 2*x^3) / (1 - x)^8 + O(x^30))) \\ _Colin Barker_, Oct 26 2017

%Y Cf. A061552, A000292.

%K easy,nonn

%O 1,4

%A _Mike Zabrocki_, Nov 05 2004

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)