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%I #78 Sep 08 2022 08:44:29
%S 7,28,112,448,1792,7168,28672,114688,458752,1835008,7340032,29360128,
%T 117440512,469762048,1879048192,7516192768,30064771072,120259084288,
%U 481036337152,1924145348608,7696581394432,30786325577728,123145302310912,492581209243648
%N a(n) = 7*4^n.
%C Subsequence of A000069, the odious numbers. - _Reinhard Zumkeller_, Aug 26 2007
%C 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
%C 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
%H Vincenzo Librandi, <a href="/A002042/b002042.txt">Table of n, a(n) for n = 0..500</a>
%H K. Chakraborty, A. Hoque, R. Sharma, <a href="https://arxiv.org/abs/1812.11874">Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations</a>, arXiv:1812.11874 [math.NT], 2018.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (4).
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 4*a(n-1), n > 0, with a(0) = 7.
%F G.f.: 7/(1-4*x). (End)
%F a(n) = 7*A000302(n). - _Michel Marcus_, Jun 24 2015
%F E.g.f.: 7*exp(4*x). - _G. C. Greubel_, Feb 18 2019
%t 7*4^Range[0, 100] (* _Vladimir Joseph Stephan Orlovsky_, Jun 09 2011 *)
%t CoefficientList[Series[7/(1-4x), {x, 0, 33}], x] (* _Vincenzo Librandi_, Jun 25 2015 *)
%t NestList[4#&,7,30] (* _Harvey P. Dale_, Mar 19 2021 *)
%o (Magma) [7*4^n: n in [0..30]]; // _Vincenzo Librandi_, May 31 2011
%o (PARI) a(n)=7<<(2*n) \\ _Charles R Greathouse IV_, Apr 17 2012
%o (Sage) [7*4^n for n in (0..30)] # _G. C. Greubel_, Feb 18 2019
%Y First differences of A083597. Bisection of A005009.
%Y Cf. A306472 (37*27^n), A009971 (27^n), A000302 (4^n), A000290 (n^2), A000578 (n^3).
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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