A098994 Number of permutations of [n] with exactly 3 descents which avoid the pattern 1324.
0, 0, 0, 1, 26, 229, 1246, 5086, 17084, 49768, 129958, 311051, 693290, 1455909, 2906436, 5554172, 10217000, 18173272, 31373636, 52731365, 86514106, 138865053, 218487442, 337533050, 512743140, 766899120, 1130650170, 1644796335, 2363118186, 3355858221, 4713974824
Offset: 1
Links
- T. D. Noe, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
Programs
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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
Formula
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.
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