This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A066373 #56 Dec 22 2024 20:02:47
%S A066373 2,7,20,52,128,304,704,1600,3584,7936,17408,37888,81920,176128,376832,
%T A066373 802816,1703936,3604480,7602176,15990784,33554432,70254592,146800640,
%U A066373 306184192,637534208,1325400064,2751463424,5704253440,11811160064,24427626496,50465865728,104152956928
%N A066373 a(n) = (3*n-2)*2^(n-3).
%C A066373 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
%C A066373 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
%H A066373 Harry J. Smith, <a href="/A066373/b066373.txt">Table of n, a(n) for n = 2..200</a>
%H A066373 M. Azaola and F. Santos, <a href="http://personales.unican.es/santosf/Articulos/">The number of triangulations of the cyclic polytope C(n,n-4)</a>, Discrete Comput. Geom., 27 (2002), 29-48.
%H A066373 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F A066373 G.f.: x^2*(2-x)/(1-2x)^2. - _Emeric Deutsch_, Jul 23 2006
%F A066373 a(n) = 2*a(n-1) +3*2^(n-3). - _Vincenzo Librandi_, Mar 20 2011
%F A066373 a(n+1) - a(n) = A098156(n). - _R. J. Mathar_, Apr 25 2013
%F A066373 From _Paul Curtz_, Jun 29 2018: (Start)
%F A066373 a(n) = A130129(n-2) - A130129(n-3) for n >= 2.
%F A066373 Binomial transform of A016789.
%F A066373 Inverse binomial transform of A288834.
%F A066373 Also the main diagonal of the difference table of m -> (-1)^m*(m+2).
%F A066373 2, -3, 4, -5, ...
%F A066373 -5, 7, -9, 11, ...
%F A066373 12, -16, 20, -24, ...
%F A066373 -28, 36, -44, 52, ... . (End)
%p A066373 seq((3*n-2)*2^(n-3),n=2..30); # _Emeric Deutsch_, Jul 23 2006
%t A066373 Array[(3 # - 2)*2^(# - 3) &, 28, 2] (* or *)
%t A066373 Drop[CoefficientList[Series[x^2*(2 - x)/(1 - 2 x)^2, {x, 0, 29}], x], 2] (* _Michael De Vlieger_, Jun 30 2018 *)
%o A066373 (PARI) a(n) = { (3*n - 2)*2^(n - 3) } /* _Harry J. Smith_, Feb 11 2010 */
%Y A066373 Column k=2 of A229079.
%Y A066373 Cf. A016789, A098156, A130129, A288834.
%K A066373 nonn,easy
%O A066373 2,1
%A A066373 _N. J. A. Sloane_, Jan 04 2002