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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
OFFSET
0,6
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
KEYWORD
nonn,easy
AUTHOR
Brian Nakamura, Apr 03 2013
STATUS
approved