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A074092 Number of plane binary trees of size n+3 and contracted height n. 3
1, 2, 8, 40, 144, 448, 1280, 3456, 8960, 22528, 55296, 133120, 315392, 737280, 1703936, 3899392, 8847360, 19922944, 44564480, 99090432, 219152384, 482344960, 1056964608, 2306867200, 5016387584, 10871635968, 23488102400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

H. Bottomley & A. Karttunen, Notes concerning diagonals of the square arrays A073345 and A073346.

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

FORMULA

a(0) = 1, a(1) = 2, a(n) = 2^(n-1)*(n+2)*(n-1) = (2^n)*(C(n, n-2)+C(n-1, n-2)) = 2^n * A000096(n-1).

a(n) = 6*a(n-1)-12*a(n-2)+8*a(n-3) for n>4. G.f.: (1-4*x+8*x^2+8*x^3-16*x^4)/(1-2*x)^3. [Colin Barker, Mar 21 2012]

For n>1, a(n) = (1/2) * Sum_{k=0..n+1} Sum_{i=0..n+1} (k-1) * C(n+1,i). - Wesley Ivan Hurt, Sep 20 2017

MAPLE

A074092 := n -> `if`((n < 2), n+1, 2^(n-1)*(n+2)*(n-1));

A074092v2 := n -> `if`((n < 2), n+1, (2^n)*(binomial(n, n-2)+binomial(n-1, n-2)));

MATHEMATICA

Table[If[n < 2, n + 1, 2^(n - 1)*(n + 2) (n - 1)], {n, 0, 26}] (* or *)

CoefficientList[Series[(1 - 4 x + 8 x^2 + 8 x^3 - 16 x^4)/(1 - 2 x)^3, {x, 0, 26}], x] (* Michael De Vlieger, Sep 22 2017 *)

PROG

(PARI) Vec((1-4*x+8*x^2+8*x^3-16*x^4)/(1-2*x)^3+O(x^99)) \\ Charles R Greathouse IV, Mar 21 2012

CROSSREFS

a(n) = A073346(n+3, n).

Sequence in context: A152458 A087971 A127919 * A003445 A181326 A220964

Adjacent sequences:  A074089 A074090 A074091 * A074093 A074094 A074095

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Aug 19 2002

STATUS

approved

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Last modified November 18 19:59 EST 2019. Contains 329288 sequences. (Running on oeis4.)