A089264 Number of permutations of length n containing exactly once 132 and 213, likewise for pattern pair (231,312).

3, 6, 17, 42, 102, 242, 564, 1296, 2944, 6624, 14784, 32768, 72192, 158208, 345088, 749568, 1622016, 3497984, 7520256, 16121856, 34471936, 73531392, 156499968, 332398592, 704643072, 1491075072, 3149922304, 6643777536, 13992198144

Offset

4,1

Links

Table of n, a(n) for n=4..32.

Aaron Robertson, Permutations restricted by two distinct patterns of length three, arXiv:math/0012029 [math.CO], 2000.

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

For n>=7, a(n) = (n^2+21*n-28)*2^(n-9).

G.f.: x^4*(x-1)^2*(2*x^3-2*x^2+6*x-3) / (2*x-1)^3. [Colin Barker, Jan 31 2013]

Mathematica

LinearRecurrence[{6, -12, 8}, {3, 6, 17, 42, 102, 242}, 40] (* Harvey P. Dale, Apr 10 2022 *)

Crossrefs

Cf. A001815.

Sequence in context: A297972 A275057 A320807 * A121399 A212421 A238428

Adjacent sequences: A089261 A089262 A089263 * A089265 A089266 A089267

Keyword

nonn,easy

Author

Ralf Stephan, Oct 30 2003

Status

approved