A224289 Number of permutations of length n containing exactly 1 occurrence of 123 and 2 occurrences of 132.

0, 0, 0, 2, 8, 26, 79, 232, 664, 1856, 5072, 13568, 35584, 91648, 232192, 579584, 1427456, 3473408, 8359936, 19922944, 47054848, 110231552, 256311296, 591921152, 1358430208, 3099590656, 7034896384, 15888023552, 35718692864, 79960211456, 178291474432, 396076515328, 876844417024

Offset

1,4

Links

Table of n, a(n) for n=1..33.

B. Nakamura, Approaches for enumerating permutations with a prescribed number of occurrences of patterns, arXiv 1301.5080, 2013.

Index entries for linear recurrences with constant coefficients, signature (8, -24, 32, -16).

Formula

a(n) = 2^(-8+n)*(-136+70*n-11*n^2+n^3) for n>3. G.f.: -x^4*(x^3-10*x^2+8*x-2) / (2*x-1)^4. - Colin Barker, Apr 14 2013

Maple

# Programs can be obtained from author's personal website.

Mathematica

LinearRecurrence[{8, -24, 32, -16}, {0, 0, 0, 2, 8, 26, 79}, 40] (* Harvey P. Dale, Jun 23 2017 *)

Crossrefs

Cf. A000079, A001787, A001815, A046718, A001793.

Sequence in context: A325926 A097040 A302237 * A124721 A279735 A103453

Adjacent sequences: A224286 A224287 A224288 * A224290 A224291 A224292

Keyword

nonn,easy

Author

Brian Nakamura, Apr 03 2013

Status

approved