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

Author

Ralf Stephan, Oct 30 2003

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A001815.

Programs

Mathematica

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

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]