A066373 a(n) = (3*n-2)*2^(n-3).

2, 7, 20, 52, 128, 304, 704, 1600, 3584, 7936, 17408, 37888, 81920, 176128, 376832, 802816, 1703936, 3604480, 7602176, 15990784, 33554432, 70254592, 146800640, 306184192, 637534208, 1325400064, 2751463424, 5704253440, 11811160064, 24427626496, 50465865728, 104152956928

Offset: 2

Author

N. J. A. Sloane, Jan 04 2002

Keywords

• nonn
• easy

Comments

An elephant sequence, see A175654. For the corner squares 16 A[5] vectors, with decimal values between 59 and 440, lead to this sequence (with a leading 1 added). For the central square these vectors lead to the companion sequence A098156 (without a(1)). - Johannes W. Meijer, Aug 15 2010

a(n) is the total number of 1's in runs of 1's of length >= 2 over all binary words with n bits. - Félix Balado, Jan 15 2024

Links

• Harry J. Smith, Table of n, a(n) for n = 2..200
• M. Azaola and F. Santos, The number of triangulations of the cyclic polytope C(n,n-4), Discrete Comput. Geom., 27 (2002), 29-48.
• Index entries for linear recurrences with constant coefficients, signature (4,-4).

Crossrefs

Column k=2 of A229079.

Cf. A016789, A098156, A130129, A288834.

Programs

Maple

seq((3*n-2)*2^(n-3),n=2..30); # Emeric Deutsch, Jul 23 2006

Mathematica

Array[(3 # - 2)*2^(# - 3) &, 28, 2] (* or *)
Drop[CoefficientList[Series[x^2*(2 - x)/(1 - 2 x)^2, {x, 0, 29}], x], 2] (* Michael De Vlieger, Jun 30 2018 *)

PARI

a(n) = { (3*n - 2)*2^(n - 3) } /* Harry J. Smith, Feb 11 2010 */

Formula

G.f.: x^2*(2-x)/(1-2x)^2. - Emeric Deutsch, Jul 23 2006

a(n) = 2*a(n-1) +3*2^(n-3). - Vincenzo Librandi, Mar 20 2011

a(n+1) - a(n) = A098156(n). - R. J. Mathar, Apr 25 2013

From Paul Curtz, Jun 29 2018: (Start)

a(n) = A130129(n-2) - A130129(n-3) for n >= 2.

Binomial transform of A016789.

Inverse binomial transform of A288834.

Also the main diagonal of the difference table of m -> (-1)^m*(m+2).

2, -3, 4, -5, ...

-5, 7, -9, 11, ...

12, -16, 20, -24, ...

-28, 36, -44, 52, ... . (End)