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

Offset: 0

Author

Clark Kimberling, Dec 11 1999

Keywords

• nonn
• easy

Comments

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

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

Examples

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

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).

Crossrefs

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

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

Programs

Magma

[6*2^n - 5: n in [0..30]]; // Vincenzo Librandi, May 18 2011

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 *)

PARI

a(n)=6*2^n-5 \\ Charles R Greathouse IV, Oct 07 2015

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) = A000079(n)*6 - 5 = A007283(n)*2 - 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) = 3 * 2^n - 5 = 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

Extensions

Simpler definition from Ralf Stephan