A005009 a(n) = 7*2^n.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

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).

Crossrefs

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), this sequence (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

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

Cf. A000120, A014311, A118416, A173787, A212191.

Programs

Haskell

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

Magma

[7*2^n:n in [0..50]]; // Vincenzo Librandi, Sep 20 2011

Mathematica

7*2^Range[0,50] (* Vladimir Joseph Stephan Orlovsky, Mar 14 2011 *)
NestList[2#&,7,30] (* Harvey P. Dale, Aug 10 2024 *)

PARI

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

SageMath

[7*2^n for n in range(51)] # G. C. Greubel, Jan 05 2023

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), for n > 0, with a(0)=7 . - Philippe Deléham, Nov 23 2008

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

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

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

E.g.f.: 7*exp(2*x). - Stefano Spezia, May 15 2021