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A224288 Number of permutations of length n containing exactly 2 occurrences of 123 and 2 occurrences of 132. 1
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 (list; graph; refs; listen; history; text; internal format)
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, 2013.

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

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

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

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Last modified March 25 22:28 EDT 2019. Contains 321477 sequences. (Running on oeis4.)