A087323 a(n) = (n+1) * 2^n - 1.

0, 3, 11, 31, 79, 191, 447, 1023, 2303, 5119, 11263, 24575, 53247, 114687, 245759, 524287, 1114111, 2359295, 4980735, 10485759, 22020095, 46137343, 96468991, 201326591, 419430399, 872415231, 1811939327, 3758096383, 7784628223, 16106127359, 33285996543, 68719476735

Offset: 0

Author

Amarnath Murthy, Sep 03 2003

Keywords

• nonn
• easy

Comments

Row sums of triangle in A018900 (without the initial 0). - Reinhard Zumkeller, Jun 24 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..3000 (corrected by Ray Chandler, Jan 19 2019)
• Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Crossrefs

Cf. A087322 (a triangle which includes this sequence as the leading diagonal but without the initial zero).

Programs

Magma

[((n+1)*2^n - 1): n in [1..30]]; // Vincenzo Librandi, Sep 29 2011

Mathematica

Table[(n + 1)2^n - 1, {n, 0, 29}] (* Alonso del Arte, Jan 31 2014 *)
LinearRecurrence[{5,-8,4},{0,3,11},40] (* Harvey P. Dale, Sep 15 2019 *)

Formula

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

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). G.f.: x*(3-4*x)/((1-x)*(1-2*x)^2). - Colin Barker, Mar 23 2012

a(n) = A001787(n+1) - 1. - Omar E. Pol, Nov 09 2013

Extensions

Edited and extended by David Wasserman, May 06 2005

Formula promoted to definition and offset adjusted to 0 by Alonso del Arte, Jan 31 2014