A159695 a(0)=7, a(n) = 2*a(n-1) + 2^(n-1) for n > 0.
7, 15, 32, 68, 144, 304, 640, 1344, 2816, 5888, 12288, 25600, 53248, 110592, 229376, 475136, 983040, 2031616, 4194304, 8650752, 17825792, 36700160, 75497472, 155189248, 318767104, 654311424, 1342177280, 2751463424, 5637144576
Offset: 0
Examples
a(0)=7, a(1) = 2*7 + 1 = 15, a(2) = 2*15 + 2 = 32, a(3) = 2*32 + 4 = 68, a(4) = 2*68 + 8 = 144, ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..3300
- Index entries for linear recurrences with constant coefficients, signature (4, -4).
Programs
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Magma
[(14+n)*2^(n-1): n in [0..30]]; // G. C. Greubel, Jun 02 2018
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Mathematica
LinearRecurrence[{4,-4}, {7,15}, 30] (* or *) Table[(14+n)*2^(n-1), {n, 0, 30}] (* G. C. Greubel, Jun 02 2018 *) nxt[{n_,a_}]:={n+1,2a+2^n}; NestList[nxt,{0,7},30][[All,2]] (* Harvey P. Dale, Jan 01 2023 *) -
PARI
for(n=0, 30, print1((14+n)*2^(n-1), ", ")) \\ G. C. Greubel, Jun 02 2018
Formula
a(n) = Sum_{k=0..n} (k+7)*binomial(n,k).
From R. J. Mathar, Apr 20 2009: (Start)
a(n) = (14+n)*2^(n-1).
a(n) = 4*a(n-1) - 4*a(n-2).
G.f.: (7-13*x)/(1-2x)^2. (End)
E.g.f.: (x+7)*exp(2*x). - G. C. Greubel, Jun 02 2018
From Amiram Eldar, Jan 19 2021: (Start)
Sum_{n>=0} 1/a(n) = 32768*log(2) - 204619418/9009.
Sum_{n>=0} (-1)^n/a(n) = 598484902/45045 - 32768*log(3/2). (End)
Extensions
More terms from R. J. Mathar, Apr 20 2009
Comments