A061761 a(n) = 2^n + 2*n - 1.

0, 3, 7, 13, 23, 41, 75, 141, 271, 529, 1043, 2069, 4119, 8217, 16411, 32797, 65567, 131105, 262179, 524325, 1048615, 2097193, 4194347, 8388653, 16777263, 33554481, 67108915, 134217781, 268435511, 536870969, 1073741883, 2147483709

Offset: 0

Author

Amarnath Murthy, May 20 2001

Keywords

• nonn

Examples

			a(5) = 2^5 + 2*5 - 1 = 32 + 10 - 1 = 41. - _Michael B. Porter_, Aug 18 2016
		

Links

• Harry J. Smith, Table of n, a(n) for n=0..200
• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A000225, A005803.

Programs

Mathematica

Table[2^n+2*n-1,{n,0,60}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)

PARI

a(n) = { 2^n + 2*n - 1 } \\ Harry J. Smith, Jul 27 2009

Formula

G.f.: x(3-5x)/((1-x)^2*(1-2x)). Binomial transform of 0,3,1,1,... (1 continued). - R. J. Mathar, Sep 17 2008

a(n) = A000225(n+1) - A005803(n), for n>0. In other words, for n>0, a(n) is the sum of the elements on the perimeter of a Pascal's triangle of depth (n+1). - Ivan N. Ianakiev, Aug 18 2016

E.g.f.: exp(x)*(exp(x) + 2*x - 1). - Stefano Spezia, Dec 08 2024