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A076616 Number of permutations of {1,2,...,n} that result in a binary search tree (when elements of the permutation are inserted in that order) of height n-1 (i.e., the second largest possible height). 6
0, 0, 0, 2, 16, 64, 208, 608, 1664, 4352, 11008, 27136, 65536, 155648, 364544, 843776, 1933312, 4390912, 9895936, 22151168, 49283072, 109051904, 240123904, 526385152, 1149239296, 2499805184, 5419040768, 11710496768, 25232932864, 54223962112, 116232552448 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

FORMULA

G.f.: 2*(4*x^2-2*x-1)*x^3/(2*x-1)^3. - Alois P. Heinz, Sep 20 2011

From Colin Barker, May 16 2016: (Start)

a(n) = 2^(n-3)*(n^2-n-4) for n>2.

a(n) = 6*a(n-1)-12*a(n-2)+8*a(n-3) for n>5.

(End)

EXAMPLE

a(3) = 2 because only the permutations (2,1,3) and (2,3,1) result in a search tree of height 2 (notice we count empty external nodes in determining the height). The largest such trees are of height 3.

MAPLE

a:= n-> `if`(n<3, 0, (<<0|1|0>, <0|0|1>, <8|-12|6>>^(n-3). <<2, 16, 64>>)[1, 1]): seq(a(n), n=0..40);  # Alois P. Heinz, Sep 20 2011

PROG

(PARI) concat(vector(3), Vec(2*x^3*(1+2*x-4*x^2)/(1-2*x)^3 + O(x^50))) \\ Colin Barker, May 16 2016

CROSSREFS

Lower diagonal of A195581.

Cf. A076615.

Sequence in context: A061608 A212899 A127276 * A222381 A110048 A094505

Adjacent sequences:  A076613 A076614 A076615 * A076617 A076618 A076619

KEYWORD

nonn,easy

AUTHOR

Jeffrey Shallit, Oct 22 2002

EXTENSIONS

More terms from Alois P. Heinz, Sep 20 2011

STATUS

approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)