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

0,2

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).

Formula

a(n) = 4*a(n-1) + 21.

G.f.: (1+20*x)/((1-x)*(1-4*x)). - R. J. Mathar, Sep 13 2008

a(n) = 10*A000975(2n) + A000975(2n+1). - Paul Curtz, Sep 17 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)

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 *)

Prog

(Magma) [8*4^n-7: n in [0..30]]; // Vincenzo Librandi, May 31 2011
(PARI) x='x+O('x^50); Vec((1+20*x)/((1-x)*(1-4*x))) \\ G. C. Greubel, Sep 30 2017

Crossrefs

Cf. A000975.

Sequence in context: A356629 A362571 A198040 * A090159 A025283 A076433

Adjacent sequences: A141719 A141720 A141721 * A141723 A141724 A141725

Keyword

nonn,easy

Author

Paul Curtz, Sep 12 2008

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

Status

approved