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%I #53 Feb 14 2024 14:11:05
%S 2,7,20,52,128,304,704,1600,3584,7936,17408,37888,81920,176128,376832,
%T 802816,1703936,3604480,7602176,15990784,33554432,70254592,146800640,
%U 306184192,637534208,1325400064,2751463424,5704253440
%N a(n) = (3*n-2)*2^(n-3).
%C 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 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 Harry J. Smith, <a href="/A066373/b066373.txt">Table of n, a(n) for n = 2..200</a>
%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F G.f.: x^2*(2-x)/(1-2x)^2. - _Emeric Deutsch_, Jul 23 2006
%F a(n) = 2*a(n-1) +3*2^(n-3). - _Vincenzo Librandi_, Mar 20 2011
%F a(n+1) - a(n) = A098156(n). - _R. J. Mathar_, Apr 25 2013
%F From _Paul Curtz_, Jun 29 2018: (Start)
%F a(n) = A130129(n-2) - A130129(n-3) for n >= 2.
%F Binomial transform of A016789.
%F Inverse binomial transform of A288834.
%F Also the main diagonal of the difference table of m -> (-1)^m*(m+2).
%F 2, -3, 4, -5, ...
%F -5, 7, -9, 11, ...
%F 12, -16, 20, -24, ...
%F -28, 36, -44, 52, ... . (End)
%p seq((3*n-2)*2^(n-3),n=2..30); # _Emeric Deutsch_, Jul 23 2006
%t Array[(3 # - 2)*2^(# - 3) &, 28, 2] (* or *)
%t Drop[CoefficientList[Series[x^2*(2 - x)/(1 - 2 x)^2, {x, 0, 29}], x], 2] (* _Michael De Vlieger_, Jun 30 2018 *)
%o (PARI) { for (n=2, 200, write("b066373.txt", n, " ", (3*n - 2)*2^(n - 3)) ) } /* _Harry J. Smith_, Feb 11 2010 */
%Y Column k=2 of A229079.
%Y Cf. A016789, A098156, A130129, A288834.
%K nonn,easy
%O 2,1
%A _N. J. A. Sloane_, Jan 04 2002
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