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A099743 Number of permutations with exactly 1 valley which avoid the pattern 1324. 1
0, 0, 2, 15, 75, 313, 1179, 4161, 14051, 45993, 147195, 463345, 1440723, 4438905, 13582955, 41350977, 125404611, 379228489, 1144370139, 3447856017, 10375942835, 31198607385, 93749962827, 281584384225, 845476670115, 2537990291433, 7617326317499 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9,-30,44,-24).

FORMULA

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

From Colin Barker, Feb 14 2017: (Start)

a(n) = -7*2^(n-3) + 3^n - 9*2^(n-4)*n - 2^(n-4)*n^2.

a(n) = 9*a(n-1) - 30*a(n-2) + 44*a(n-3) - 24*a(n-4) for n>4.

(End)

EXAMPLE

a(3) = 2 because 213 and 312 have exactly 1 valley and avoid 1324.

PROG

(PARI) concat(vector(2), Vec(x^3*(2-3*x) / ((1-2*x)^3*(1-3*x)) + O(x^30))) \\ Colin Barker, Feb 14 2017

CROSSREFS

Cf. A000079.

Sequence in context: A268644 A178321 A007232 * A283842 A102289 A041243

Adjacent sequences:  A099740 A099741 A099742 * A099744 A099745 A099746

KEYWORD

nonn,easy

AUTHOR

Mike Zabrocki, Nov 09 2004

STATUS

approved

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Last modified October 23 01:57 EDT 2018. Contains 316518 sequences. (Running on oeis4.)