A142974 A007318 * [1, 1, -1, 1, 1, 1, ...].

1, 2, 2, 2, 4, 12, 34, 86, 200, 440, 934, 1938, 3964, 8036, 16202, 32558, 65296, 130800, 261838, 523946, 1048196, 2096732, 4193842, 8388102, 16776664, 33553832, 67108214, 134217026, 268434700, 536870100, 1073740954, 2147482718

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

Binomial transform of [1, 1, -1, 1, 1, 1, ...].

From R. J. Mathar, Jul 31 2008: (Start)

O.g.f.: x(1-3x+x^2+3x^3)/((1-x)^3*(1-2x)).

a(n) = 4n - 2 - 2*A000217(n) + 2^(n-1). (End)

a(n) = 2^n - n(n-1) (if offset is 0). - Emeric Deutsch, Aug 09 2008

Example

a(6) = 12 = (1, 5, 10, 10, 5, 1) dot (1, 1, -1, 1, 1, 1) = (1 + 5 - 10 + 10, + 5, + 1).

Maple

a:=proc(n) options operator, arrow: 2^n-n*(n-1) end proc: seq(a(n), n=0..32); # Emeric Deutsch, Aug 09 2008

Mathematica

Table[2^n-n(n-1), {n, 0, 3*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2010 *)

Crossrefs

Sequence in context: A260786 A067920 A107902 * A259856 A279805 A123914

Adjacent sequences: A142971 A142972 A142973 * A142975 A142976 A142977

Keyword

nonn

Author

Gary W. Adamson, Jul 15 2008

Extensions

More terms from Emeric Deutsch, Aug 09 2008

Status

approved