A048488 a(n) = 6*2^n - 5.

1, 7, 19, 43, 91, 187, 379, 763, 1531, 3067, 6139, 12283, 24571, 49147, 98299, 196603, 393211, 786427, 1572859, 3145723, 6291451, 12582907, 25165819, 50331643, 100663291, 201326587, 402653179, 805306363, 1610612731, 3221225467, 6442450939, 12884901883, 25769803771

Offset

0,2

Comments

Original name: a(n) = T(5,n), array T given by A048483.

n-th difference of a(n), a(n-1), ..., a(0) is (6, 6, 6, ...).

Sequence is generated by the Northwest (NW) direction of circles put around circle(s). See illustration. - Odimar Fabeny, Aug 09 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Odimar Fabeny, Illustration for this sequence.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

a(n) = 2*a(n-1) + 5, n > 0, a(0) = 1. - Paul Barry, Aug 25 2004

Equals binomial transform of [1, 6, 6, 6, ...]. - Gary W. Adamson, Apr 29 2008

a(n) = 6*A000079(n) - 5 = 2*A007283(n) - 5. - Omar E. Pol, Dec 21 2008

From Colin Barker, Sep 17 2012: (Start)

a(n) = 3*2^(1+n) - 5.

a(n) = 3*a(n-1) - 2*a(n-2).

G.f.: (1+4*x)/((1-x)*(1-2*x)). (End)

a(n+1) = 1 + 2*(Sum_{i=0..n-1} 3i) for n > 0. - Gerasimov Sergey and Alonso del Arte, May 03 2014

a(n) = A000225(n+1) + 4*A000225(n). - R. J. Mathar, Feb 27 2019

From Elmo R. Oliveira, Nov 01 2025: (Start)

E.g.f.: (6*exp(x) - 5)*exp(x).

a(n) = (3*A000918(n+2) - 4)/2. (End)

Example

a(2) = 6 * 2^2 - 5 = 6 * 4 - 5 = 24 - 5 = 19.
a(3) = 6 * 2^3 - 5 = 6 * 8 - 5 = 48 - 5 = 43.

Maple

A048488:=n->6*2^n - 5; seq(A048488(n), n=0..30); # Wesley Ivan Hurt, May 09 2014

Mathematica

6(2^Range[0, 35]) - 5 (* Alonso del Arte, May 03 2014 *)

Prog

(Magma) [6*2^n - 5: n in [0..30]]; // Vincenzo Librandi, May 18 2011
(PARI) a(n)=6*2^n-5 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A000225, A000918, A048483.

Cf. A000079, A007283. - Omar E. Pol, Dec 21 2008

Sequence in context: A054691 A139828 A247905 * A155303 A268801 A155275

Adjacent sequences: A048485 A048486 A048487 * A048489 A048490 A048491

Keyword

nonn,easy

Author

Clark Kimberling, Dec 11 1999

Extensions

Simpler definition from Ralf Stephan

Status

approved