

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
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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^n2) = A000079(n)*(A000079(n)  2) = A159786(2^n) = 8*A006516(n1), n>=1.
G.f.: 8*x^2 / ((12*x)*(14*x)).  Colin Barker, Mar 30 2016
a(n) = 6*a(n1)8*a(n2) 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/((12*x)*(14*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



