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A098992 Number of permutations of [n] with exactly 2 descents which avoid the pattern 1324. 1
0, 0, 1, 11, 55, 190, 526, 1254, 2682, 5280, 9735, 17017, 28457, 45838, 71500, 108460, 160548, 232560, 330429, 461415, 634315, 859694, 1150138, 1520530, 1988350, 2574000, 3301155, 4197141, 5293341, 6625630, 8234840, 10167256, 12475144, 15217312, 18459705 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

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

From Colin Barker, Oct 26 2017: (Start)

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

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.

(End)

PROG

(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

CROSSREFS

Cf. A061552, A000292.

Sequence in context: A226255 A022606 A072025 * A246990 A156589 A165791

Adjacent sequences:  A098989 A098990 A098991 * A098993 A098994 A098995

KEYWORD

easy,nonn

AUTHOR

Mike Zabrocki, Nov 05 2004

STATUS

approved

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Last modified October 22 06:54 EDT 2019. Contains 328315 sequences. (Running on oeis4.)