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 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

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Last modified July 13 10:38 EDT 2020. Contains 335687 sequences. (Running on oeis4.)