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A098994 Number of permutations of [n] with exactly 3 descents which avoid the pattern 1324. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 26 12:04 EDT 2021. Contains 347665 sequences. (Running on oeis4.)