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

1,5

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).

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

Prog

(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

Crossrefs

Cf. A061552, A000292.

Sequence in context: A220714 A159519 A110486 * A172124 A196633 A196638

Adjacent sequences: A098991 A098992 A098993 * A098995 A098996 A098997

Keyword

easy,nonn

Author

Mike Zabrocki, Nov 05 2004

Status

approved