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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A211012 Total area of all squares and rectangles after 2^n stages in the toothpick structure of A139250, assuming the toothpicks have length 2. 6
0, 0, 8, 48, 224, 960, 3968, 16128, 65024, 261120, 1046528, 4190208, 16769024, 67092480, 268402688, 1073676288, 4294836224, 17179607040, 68718952448, 274876858368, 1099509530624, 4398042316800, 17592177655808, 70368727400448, 281474943156224 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.

Similar to A271061. - Robert Price, Mar 30 2016

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

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

FORMULA

a(n) = 2^n * (2^n-2) = A000079(n)*(A000079(n) - 2) = A159786(2^n) = 8*A006516(n-1), n>=1.

G.f.: 8*x^2 / ((1-2*x)*(1-4*x)). - Colin Barker, Mar 30 2016

a(n) = 6*a(n-1)-8*a(n-2) for n>2. - Colin Barker, Mar 30 2016

EXAMPLE

For n = 3 the area of all squares and rectangles in the toothpick structure after 2^3 stages equals the area of a rectangle of size 8X6, so a(3) = 8*6 = 48.

PROG

(PARI) concat(vector(2), Vec(8*x^2/((1-2*x)*(1-4*x)) + O(x^50))) \\ Colin Barker, Mar 30 2016

CROSSREFS

Row sums of triangle A211017, n>=1.

Cf. A000079, A006516, A139250, A159786, A160124, A211008, A211016, A211018.

Sequence in context: A261975 A087914 A271061 * A081084 A230931 A073390

Adjacent sequences:  A211009 A211010 A211011 * A211013 A211014 A211015

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Sep 21 2012

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)