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%I #56 Jan 06 2023 09:05:51
%S 7,14,28,56,112,224,448,896,1792,3584,7168,14336,28672,57344,114688,
%T 229376,458752,917504,1835008,3670016,7340032,14680064,29360128,
%U 58720256,117440512,234881024,469762048,939524096,1879048192,3758096384
%N a(n) = 7*2^n.
%C The first differences are the sequence itself. - _Alexandre Wajnberg_ & _Eric Angelini_, Sep 07 2005
%H Vincenzo Librandi, <a href="/A005009/b005009.txt">Table of n, a(n) for n = 0..3000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F G.f.: 7/(1-2*x).
%F a(n) = A118416(n+1,4) for n > 3. - _Reinhard Zumkeller_, Apr 27 2006
%F a(n) = 2*a(n-1), for n > 0, with a(0)=7 . - _Philippe Deléham_, Nov 23 2008
%F a(n) = 7 * A000079(n). - _Omar E. Pol_, Dec 16 2008
%F a(n) = A173787(n+3,n). - _Reinhard Zumkeller_, Feb 28 2010
%F 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
%F 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
%F E.g.f.: 7*exp(2*x). - _Stefano Spezia_, May 15 2021
%t 7*2^Range[0,50] (* _Vladimir Joseph Stephan Orlovsky_, Mar 14 2011 *)
%o (Magma) [7*2^n:n in [0..50]]; // _Vincenzo Librandi_, Sep 20 2011
%o (PARI) a(n)=7<<n \\ _Charles R Greathouse IV_, Dec 22 2011
%o (Haskell) a005009 = (* 7) . (2 ^) -- _Reinhard Zumkeller_, May 03 2012
%o (SageMath) [7*2^n for n in range(51)] # _G. C. Greubel_, Jan 05 2023
%Y 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).
%Y Row sums of (6, 1)-Pascal triangle A093563 and of (1, 6)-Pascal triangle A096956, n>=1.
%Y Cf. A000120, A014311, A118416, A173787, A212191.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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