A002042 a(n) = 7*4^n.

7, 28, 112, 448, 1792, 7168, 28672, 114688, 458752, 1835008, 7340032, 29360128, 117440512, 469762048, 1879048192, 7516192768, 30064771072, 120259084288, 481036337152, 1924145348608, 7696581394432, 30786325577728, 123145302310912, 492581209243648

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

First differences of A083597. Bisection of A005009.

Cf. A306472 (37*27^n), A009971 (27^n), A000302 (4^n), A000290 (n^2), A000578 (n^3).

Programs

Magma

[7*4^n: n in [0..30]]; // Vincenzo Librandi, May 31 2011

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 *)

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

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