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A356728
The number of 3-permutations that avoid the patterns 132 and 213.
0
1, 4, 12, 28, 58, 114, 220, 424, 822, 1606, 3160, 6252, 12418, 24730, 49332, 98512, 196846, 393486, 786736, 1573204, 3146106, 6291874, 12583372, 25166328, 50332198, 100663894, 201327240, 402653884, 805307122, 1610613546, 3221226340
OFFSET
1,2
FORMULA
a(n) = A308580(n-1) - 2.
a(n) = a(n-1) + 3*2^(n-2) + 2*(n-2).
From Stefano Spezia, Aug 27 2022: (Start)
G.f.: x*(1 - x + x^2 - 3*x^3)/((1 - x)^3*(1 - 2*x)).
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n > 4.
a(n) = 3*2^(n-1) + n^2 - 3*n. (End)
MATHEMATICA
LinearRecurrence[{5, -9, 7, -2}, {1, 4, 12, 28}, {1, 35}] (* Hugo Pfoertner, Aug 27 2022 *)
CROSSREFS
Cf. A308580.
Sequence in context: A011939 A203286 A028346 * A079089 A182705 A186924
KEYWORD
nonn,easy
AUTHOR
Nathan Sun, Aug 24 2022
STATUS
approved