OFFSET
2,1
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).
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)
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)
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 *)
PROG
(PARI) { for (n=2, 200, write("b066373.txt", n, " ", (3*n - 2)*2^(n - 3)) ) } /* Harry J. Smith, Feb 11 2010 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 04 2002
STATUS
approved