A158879 a(n) = 4^n + n.
1, 5, 18, 67, 260, 1029, 4102, 16391, 65544, 262153, 1048586, 4194315, 16777228, 67108877, 268435470, 1073741839, 4294967312, 17179869201, 68719476754, 274877906963, 1099511627796, 4398046511125, 17592186044438, 70368744177687
Offset: 0
Examples
a(0)=4^0+0 = 1, a(1)=4^1+1 = 5, a(2)=4^2+2 = 18, a(3)=4^3+3 = 67, ...
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
- Index entries for linear recurrences with constant coefficients, signature (6,-9,4).
Programs
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GAP
List([0..30], n-> n+4^n); # G. C. Greubel, Mar 04 2020
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Magma
[4^n+n: n in [0..30]]; // Vincenzo Librandi, Jun 16 2013
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Maple
seq( 4^n+n, n=0..30); # G. C. Greubel, Mar 04 2020
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Mathematica
Table[4^n+n,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *) CoefficientList[Series[(1-x-3x^2)/((1-4x)(1-x)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 16 2013 *) LinearRecurrence[{6,-9,4},{1,5,18},30] (* Harvey P. Dale, Jun 02 2016 *) -
PARI
a(n)=4^n+n \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[n+4^n for n in (0..30)] # G. C. Greubel, Mar 04 2020
Formula
G.f.: (1 - x - 3*x^2)/((1-4*x)*(1-x)^2). - R. J. Mathar, Mar 29 2009
a(n) = 6*a(n-1) -9*a(n-2) +4*a(n-3). - R. J. Mathar, Mar 29 2009
E.g.f.: x*exp(x) + exp(4*x). - G. C. Greubel, Mar 04 2020
Extensions
Corrected typo in a(22) from R. J. Mathar, Mar 29 2009