A141722 a(n) = 8*4^n - 7.
1, 25, 121, 505, 2041, 8185, 32761, 131065, 524281, 2097145, 8388601, 33554425, 134217721, 536870905, 2147483641, 8589934585, 34359738361, 137438953465, 549755813881, 2199023255545, 8796093022201, 35184372088825, 140737488355321, 562949953421305
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)
- Index entries for linear recurrences with constant coefficients, signature (5,-4).
Crossrefs
Cf. A000975.
Programs
-
Magma
[8*4^n-7: n in [0..30]]; // Vincenzo Librandi, May 31 2011
-
Maple
A141722:=n->8*4^n-7; seq(A141722(n), n=0..30); # Wesley Ivan Hurt, Feb 15 2014
-
Mathematica
Table[8*4^n-7, {n, 0, 30}] (* Wesley Ivan Hurt, Feb 15 2014 *) -
PARI
x='x+O('x^50); Vec((1+20*x)/((1-x)*(1-4*x))) \\ G. C. Greubel, Sep 30 2017
Formula
a(n) = 4*a(n-1) + 21.
G.f.: (1+20*x)/((1-x)*(1-4*x)). - R. J. Mathar, Sep 13 2008
From G. C. Greubel, Sep 30 2017: (Start)
a(n) = 5*a(n-1) - 4*a(n-2).
E.g.f.: 8*exp(4*x) - 7*exp(x). (End)
Extensions
Edited by N. J. A. Sloane, Sep 13 2008
More terms from R. J. Mathar, Sep 13 2008
More terms from Vincenzo Librandi, May 31 2011
Better name (using formula from R. J. Mathar) from Joerg Arndt, Feb 16 2014