cp's OEIS Frontend

A098994 Number of permutations of [n] with exactly 3 descents which avoid the pattern 1324.

%I A098994 #10 Oct 26 2017 06:24:46
%S A098994 0,0,0,1,26,229,1246,5086,17084,49768,129958,311051,693290,1455909,
%T A098994 2906436,5554172,10217000,18173272,31373636,52731365,86514106,
%U A098994 138865053,218487442,337533050,512743140,766899120,1130650170,1644796335,2363118186,3355858221,4713974824
%N A098994 Number of permutations of [n] with exactly 3 descents which avoid the pattern 1324.
%H A098994 T. D. Noe, <a href="/A098994/b098994.txt">Table of n, a(n) for n = 1..1000</a>
%H A098994 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
%F A098994 G.f.: x^4*(1 + 14*x - 17*x^2 - 6*x^3 + 23*x^4 - 14*x^5 + 3*x^6) / (1 - x)^12.
%F A098994 a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>12. - _Colin Barker_, Oct 26 2017
%o A098994 (PARI) concat(vector(3), Vec(x^4*(1 + 14*x - 17*x^2 - 6*x^3 + 23*x^4 - 14*x^5 + 3*x^6) / (1 - x)^12 + O(x^40))) \\ _Colin Barker_, Oct 26 2017
%Y A098994 Cf. A061552, A000292.
%K A098994 easy,nonn
%O A098994 1,5
%A A098994 _Mike Zabrocki_, Nov 05 2004