A224288 Number of permutations of length n containing exactly 2 occurrences of 123 and 2 occurrences of 132.

0, 0, 0, 0, 1, 6, 26, 94, 306, 934, 2732, 7752, 21488, 58432, 156288, 411904, 1071104, 2750976, 6984704, 17545216, 43634688, 107511808, 262602752, 636223488, 1529741312, 3652059136, 8660975616, 20412104704, 47826599936, 111446851584, 258360737792, 596044152832

Offset

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

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

B. Nakamura, A Maple package for enumerating n-permutations with r occurrences of the pattern 123 and s occurrences of the pattern 132 [Broken link]

Index entries for linear recurrences with constant coefficients, signature (10,-40,80,-80,32).

Formula

G.f.: -(2*x^5+6*x^4-6*x^3+6*x^2-4*x+1)*x^4/(2*x-1)^5. - Alois P. Heinz, Apr 03 2013

a(n) = 2^(-11+n)*(1504-994*n+219*n^2-18*n^3+n^4) for n>4. - Colin Barker, Apr 14 2013

Example

a(4) = 1: (1,2,4,3).
a(5) = 6: (2,3,5,1,4), (2,3,5,4,1), (2,5,1,3,4), (3,1,4,5,2), (4,1,2,5,3), (5,1,2,4,3).

Maple

# Programs can be obtained from the Nakamura link

Mathematica

Join[{0, 0, 0, 0, 1}, LinearRecurrence[{10, -40, 80, -80, 32}, {6, 26, 94, 306, 934}, 27]] (* Jean-François Alcover, Feb 29 2020 *)

Crossrefs

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

Sequence in context: A032196 A011780 A036631 * A036638 A036645 A000393

Adjacent sequences: A224285 A224286 A224287 * A224289 A224290 A224291

Keyword

nonn,easy

Author

Brian Nakamura, Apr 03 2013

Status

approved