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A005009 7*2^n. 31
7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The first differences are the sequence itself. - Alexandre Wajnberg & Eric Angelini, Sep 07 2005

a(n) = A173787(n+3,n). [Reinhard Zumkeller, Feb 28 2010]

Intersection of A014311 and A212191: all terms and their squares are the sum of exactly three distinct powers of 2, A000120(a(n)) = A000120(a(n)^2) = 3; [Reinhard Zumkeller, May 03 2012]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (2).

FORMULA

G.f.: 7/(1-2*x).

a(n) = A118416(n+1,4) for n>3. - Reinhard Zumkeller, Apr 27 2006

a(n)=2*a(n-1), n>0 ; a(0)=7 . [Philippe Deléham, Nov 23 2008]

a(n) = 7 * A000079(n). [Omar E. Pol, Dec 16 2008]

G.f.: 2/x/G(0) - 1/x + 9, where G(k)= 1 + 1/(1 - x*(7*k+2)/(x*(7*k+9) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013

MATHEMATICA

7*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)

PROG

(MAGMA) [7*2^n:n in [0..30]]; // Vincenzo Librandi, Sep 20 2011

(PARI) a(n)=7<<n \\ Charles R Greathouse IV, Dec 22 2011

(Haskell)

a005009 = (* 7) . (2 ^) -- Reinhard Zumkeller, May 03 2012

CROSSREFS

Row sums of (6, 1)-Pascal triangle A093563 and of (1, 6)-Pascal triangle A096956, n>=1.

Cf. A000079. [From Omar E. Pol, Dec 16 2008]

Sequence in context: A033895 A196876 A115876 * A135092 A245417 A058530

Adjacent sequences:  A005006 A005007 A005008 * A005010 A005011 A005012

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified November 20 10:50 EST 2017. Contains 294963 sequences.