login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085354 3*4^n-(n+4)*2^(n-1). 2
1, 7, 36, 164, 704, 2928, 11968, 48448, 195072, 783104, 3138560, 12567552, 50298880, 201256960, 805158912, 3220914176, 12884246528, 51538231296, 206155546624, 824627691520, 3298522300416, 13194113318912, 52776503607296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A060188.

The depth i nodes of a perfect binary tree are numbered 2^i through 2^(i+1) - 1, so that the root has number 1, depth 1 nodes have numbers 2 and 3, depth 2 nodes have numbers 4, 5, 6 and 7 and so on. We sum all the numbers in the path connecting a leaf node to the root. For a height n tree, a(n) is the sum of these sums for all leaves nodes. So for instance a height 1 tree has paths 1, 2 and 1, 3 connecting the root to the leaves, and (1+2) + (1+3) = a(1) = 7. This interpretation suggests a recursive formula for computing a(n) by completing the paths covered in a(n-1) and adding the leaves. - Jean M. Morales, Oct 24 2013

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to sequences with linear recurrences with constant coefficients, signature (8,-20,16).

FORMULA

a(n) = sum{m = 2^n..2^(n+1)} A005187(m). a(n) = 2^n*(2^(n+1)-1) + sum_{k = 0..(n-1)} a(k) . - Philippe Deléham, Feb 19 2004

G.f.: (1-x)/((1-4*x)*(1-2*x)^2).  - Bruno Berselli, Sep 05 2011

a(n) = 2*a(n-1) + 3*2^(2n-1) - 2^(n-1), a(0) = 1 - Jean M. Morales, Oct 24 2013

MATHEMATICA

Table[3 * 4^n - (n + 4) * 2^(n - 1), {n, 0, 19}] (* Alonso del Arte, Oct 23 2013 *)

PROG

(MAGMA) [3*4^n-(n+4)*2^(n-1): n in [0..30]]; // Vincenzo Librandi, Sep 05 2011

CROSSREFS

Sequence in context: A243037 A181292 A026018 * A051198 A003516 A095931

Adjacent sequences:  A085351 A085352 A085353 * A085355 A085356 A085357

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Jun 24 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 18 15:54 EST 2014. Contains 252163 sequences.