OFFSET
0,1
COMMENTS
Subsequence of A000069, the odious numbers. - Reinhard Zumkeller, Aug 26 2007
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
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
K. Chakraborty, A. Hoque, R. Sharma, Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations, arXiv:1812.11874 [math.NT], 2018.
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (4).
FORMULA
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 4*a(n-1), n > 0, with a(0) = 7.
G.f.: 7/(1-4*x). (End)
a(n) = 7*A000302(n). - Michel Marcus, Jun 24 2015
E.g.f.: 7*exp(4*x). - G. C. Greubel, Feb 18 2019
MATHEMATICA
7*4^Range[0, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
CoefficientList[Series[7/(1-4x), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 25 2015 *)
NestList[4#&, 7, 30] (* Harvey P. Dale, Mar 19 2021 *)
PROG
(Magma) [7*4^n: n in [0..30]]; // Vincenzo Librandi, May 31 2011
(PARI) a(n)=7<<(2*n) \\ Charles R Greathouse IV, Apr 17 2012
(Sage) [7*4^n for n in (0..30)] # G. C. Greubel, Feb 18 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved