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 A187297 #51 Sep 02 2025 22:49:15
%S A187297 0,4,18,40,70,108,154,208,270,340,418,504,598,700,810,928,1054,1188,
%T A187297 1330,1480,1638,1804,1978,2160,2350,2548,2754,2968,3190,3420,3658,
%U A187297 3904,4158,4420,4690,4968,5254,5548,5850,6160,6478,6804,7138,7480,7830,8188,8554
%N A187297 Number of 2-step one space leftwards or up, two space rightwards or down asymmetric rook's tours on an n X n board summed over all starting positions.
%C A187297 Row 2 of A187296.
%C A187297 For n>=2, a(n) equals the absolute value of 2^n times the x-coefficient of the characteristic polynomial of the n X n matrix with 1/2's along the main diagonal and 1's everywhere else (see Mathematica code below). - _John M. Campbell_, Jun 21 2011
%C A187297 If (n,2) is an arrangement of n pairs of parallel lines in general position (no two lines from distinct pairs are parallel and no three lines from distinct pairs intersect) then a(n) gives the number of bounded edges in the arrangement. Wetzel and Alexanderson refer to this arrangement as plaid in general position. - _Anthony Hernandez_, Aug 08 2016
%H A187297 R. H. Hardin and Vincenzo Librandi, <a href="/A187297/b187297.txt">Table of n, a(n) for n = 1..1000</a> (first 50 terms from R. H. Hardin)
%H A187297 G. L. Alexanderson and John E. Wetzel, <a href="http://dx.doi.org/10.1090/S0002-9947-1985-0797066-2">Divisions of Space by Parallels</a>, Transactions of the American Mathematical Society, Volume 291, Number 1 (September 1985), 366-377.
%H A187297 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A187297 Empirical: a(n) = 4*n^2 - 6*n = 2*A014107(n) for n>1 (this is now known to be correct - see other comments).
%F A187297 a(n) = +3*a(n-1) -3*a(n-2) +1*a(n-3).
%F A187297 G.f.: 2*x^2*(2+3*x-x^2)/(1-x)^3.
%t A187297 Table[Abs[ 2^(n)*Coefficient[ CharacteristicPolynomial[ Array[KroneckerDelta[#1, #2]*(1/2 - 1) + 1 &, {n, n}], x], x]], {n, 2, 55}] (* _John M. Campbell_, Jun 21 2011 *)
%t A187297 Table[If[n == 0, 0, n + n^2 - 2], {n, 0, 200, 2}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 26 2011 *)
%t A187297 CoefficientList[Series[2 x (2 + 3 x - x^2)/(1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Feb 08 2014 *)
%o A187297 (PARI) a(n)=if(n>1, 4*n^2-6*n, 0) \\ _Charles R Greathouse IV_, Aug 08 2016
%K A187297 nonn,easy,changed
%O A187297 1,2
%A A187297 _R. H. Hardin_, Mar 08 2011