A014844 a(n) = 2^n - n*(n-1)/2.

1, 2, 3, 5, 10, 22, 49, 107, 228, 476, 979, 1993, 4030, 8114, 16293, 32663, 65416, 130936, 261991, 524117, 1048386, 2096942, 4194073, 8388355, 16776940, 33554132, 67108539, 134217377, 268435078, 536870506, 1073741389, 2147483183

Offset

0,2

Comments

a(n) is the number of subsets of {1,2,...,n} that do not have a cardinality of 2. - Geoffrey Critzer, Feb 25 2012

Links

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

Index entries for linear recurrences with constant coefficients, signature (5, -9, 7, -2).

Formula

E.g.f.: exp(x)*(exp(x)-x^2/2!). - Geoffrey Critzer, Feb 25 2012

G.f.: (1-3*x+2*x^2+x^3)/((1-x)^3*(1-2*x)). - Colin Barker, Apr 01 2012

Mathematica

nn = 20; Range[0, nn]! CoefficientList[Series[Exp[x] (Exp[x] - x^2/2!), {x, 0, nn}], x] (* Geoffrey Critzer, Feb 25 2012 *)
CoefficientList[Series[(1-3*x+2*x^2+x^3)/((1-x)^3*(1-2*x)), {x, 0, 33}], x] (* Vincenzo Librandi, Apr 18 2012 *)

Prog

(Magma) [2^n - n*(n-1)/2: n in [0..40]]; // Vincenzo Librandi, Apr 18 2012

Crossrefs

Sequence in context: A001646 A103595 A293842 * A307264 A329244 A173271

Adjacent sequences: A014841 A014842 A014843 * A014845 A014846 A014847

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved