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A002063 a(n) = 9*4^n. 22
9, 36, 144, 576, 2304, 9216, 36864, 147456, 589824, 2359296, 9437184, 37748736, 150994944, 603979776, 2415919104, 9663676416, 38654705664, 154618822656, 618475290624, 2473901162496, 9895604649984, 39582418599936, 158329674399744, 633318697598976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) is twice the area of the trapezoid created by the four points (2^n,2^(n+1)), (2^(n+1), 2^n),  (2^(n+1), 2^(n+2)),  (2^(n+2), 2^(n+1)). - J. M. Bergot, May 23 2014

These are squares that can be expressed as sum of exactly two distinct powers of two. For instance, a(4) = 9*4^4 = 2304 = 2^11 + 2^8 .

It is conjectured that these are the only squares with this characteristic(tested on squares up to (10^7)^2 . - Andres Cicuttin, Apr 23 2016

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

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; a(0)=9.

G.f.: 9/(1-4*x). (End)

a(n) = 9*A000302(n). - Michel Marcus, Apr 23 2016

E.g.f.: 9*exp(4*x). - Ilya Gutkovskiy, Apr 23 2016

a(n) = 2^(2n+3) + 2^(2n). - Andres Cicuttin, Apr 26 2016

a(n) = A004171(n+1) + A000302(n). - Zhandos Mambetaliyev, Nov 19 2016

MATHEMATICA

9*4^Range[0, 100] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

PROG

(MAGMA) [9*4^n: n in [0..30]]; // Vincenzo Librandi, May 19 2011

(PARI) a(n)=9<<n \\ Charles R Greathouse IV, Apr 17 2012

CROSSREFS

Essentially the same as A055841. First differences of A002001.

Cf. A000302.

Sequence in context: A034557 A231431 A264515 * A075674 A245416 A265837

Adjacent sequences:  A002060 A002061 A002062 * A002064 A002065 A002066

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified December 10 07:51 EST 2016. Contains 278994 sequences.