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7, 28, 112, 448, 1792, 7168, 28672, 114688, 458752, 1835008, 7340032, 29360128, 117440512, 469762048, 1879048192, 7516192768, 30064771072, 120259084288, 481036337152, 1924145348608, 7696581394432, 30786325577728, 123145302310912, 492581209243648
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internal format)
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OFFSET
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0,1
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COMMENTS
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A rectangular prism with edge lengths 2^n, 2^(n+1) and 2^(n+2) has a surface area 2* (2^n*2^(n+1) + 2^(n+1)*2^(n+2) + 2^n*2^(n+2)) which equals 4*a(n). - J. M. Bergot, Aug 07 2013
x = A306472(n) and y = a(n) satisfy the Lebesgue-Ramanujan-Nagell equation x^2 + 3^(6*n+1) = 4*y^3 (see Theorem 2.1 in Chakraborty, Hoque and Sharma). - Stefano Spezia, Feb 18 2019
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LINKS
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FORMULA
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a(n) = 4*a(n-1), n > 0, with a(0) = 7.
G.f.: 7/(1-4*x). (End)
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MATHEMATICA
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CoefficientList[Series[7/(1-4x), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 25 2015 *)
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PROG
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CROSSREFS
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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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