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A211012
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Total area of all squares and rectangles after 2^n stages in the toothpick structure of A139250, assuming the toothpicks have length 2.
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7
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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
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0,3
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COMMENTS
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All internal regions in the toothpick structure are squares and rectangles. The area of every internal region is a power of 2.
For n=3,5,..., also the number of minimum vertex colorings in the n-sunlet graph. - Eric W. Weisstein, Mar 03 2024
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LINKS
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FORMULA
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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
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EXAMPLE
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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.
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PROG
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(PARI) concat(vector(2), Vec(8*x^2/((1-2*x)*(1-4*x)) + O(x^50))) \\ Colin Barker, Mar 30 2016
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CROSSREFS
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Row sums of triangle A211017, n>=1.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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