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 A035006 #93 Aug 02 2023 14:48:01
%S A035006 0,8,36,96,200,360,588,896,1296,1800,2420,3168,4056,5096,6300,7680,
%T A035006 9248,11016,12996,15200,17640,20328,23276,26496,30000,33800,37908,
%U A035006 42336,47096,52200,57660,63488,69696,76296,83300,90720,98568,106856
%N A035006 Number of possible rook moves on an n X n chessboard.
%C A035006 Obviously A035005(n) = A002492(n-1) + a(n) since Queen = Bishop + Rook. - _Johannes W. Meijer_, Feb 04 2010
%C A035006 X values of solutions of the equation: (X-Y)^3-2*X*Y=0. Y values are b(n)=2*n*(n-1)^2 (see A181617). - _Mohamed Bouhamida_, Jul 06 2023
%D A035006 E. Bonsdorff, K. Fabel and O. Riihimaa, Schach und Zahl (Chess and numbers), Walter Rau Verlag, Dusseldorf, 1966.
%H A035006 Vincenzo Librandi, <a href="/A035006/b035006.txt">Table of n, a(n) for n = 1..1000</a>
%H A035006 Alexander M. Haupt, <a href="https://arxiv.org/abs/2007.01018">Bijective enumeration of rook walks</a>, arXiv:2007.01018 [math.CO], 2020.
%H A035006 M. Janjic and B. Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 13 2013
%H A035006 M. Janjic and B. Petkovic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Janjic/janjic45.html">A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers</a>, J. Int. Seq. 17 (2014) # 14.3.5.
%H A035006 Richard P. Stanley, <a href="http://www-math.mit.edu/~rstan/bij.pdf">Bijective Proof Problems</a>, Problem 540 p. 63, (2015).
%H A035006 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A035006 a(n) = (n-1)*2*n^2.
%F A035006 a(n) = Sum_{j=1..n} ((n+j-1)^2 - (n-j+1)^2). - _Zerinvary Lajos_, Sep 13 2006
%F A035006 1/a(n+1) = Integral_{x=1/(n+1)..1/n} x*h(x) = Integral_{x=1/(n+1)..1/n} x*(1/x - floor(1/x)) = 1/((2*(n^2+2*n+1))*n) and Sum_{n>=1} 1/((2*(n^2+2*n+1))*n) = 1-Zeta(2)/2 where h(x) is the Gauss (continued fraction) map h(x)={x^-1} and {x} is the fractional part of x. - _Stephen Crowley_, Jul 24 2009
%F A035006 a(n) = 4 * A006002(n-1). - _Johannes W. Meijer_, Feb 04 2010
%F A035006 G.f.: 4*x^2*(2+x)/(1-x)^4. - _Colin Barker_, Mar 11 2012
%F A035006 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(1)=0, a(2)=8, a(3)=36, a(4)=96. - _Harvey P. Dale_, May 12 2012
%F A035006 a(n) = A006566(n) - A006564(n). - _Peter M. Chema_, Feb 10 2016
%F A035006 E.g.f.: 2*exp(x)*x^2*(2 + x). - _Stefano Spezia_, May 10 2022
%F A035006 From _Amiram Eldar_, May 14 2022: (Start)
%F A035006 Sum_{n>=2} 1/a(n) = 1 - Pi^2/12.
%F A035006 Sum_{n>=2} (-1)^n/a(n) = Pi^2/24 + log(2) - 1. (End)
%e A035006 On a 3 X 3-board, rook has 9*4 moves, so a(3)=36.
%t A035006 Table[(n-1) 2 n^2,{n,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,8,36,96},40] (* _Harvey P. Dale_, May 12 2012 *)
%o A035006 (Magma) [(n-1)*2*n^2: n in [1..40]]; // _Vincenzo Librandi_, Jun 16 2011
%Y A035006 Cf. A033586 (King), A035005 (Queen), A035008 (Knight), A002492 (Bishop) and A049450 (Pawn).
%Y A035006 Cf. A006002, A006564, A006566.
%K A035006 easy,nonn,nice
%O A035006 1,2
%A A035006 Ulrich Schimke (ulrschimke(AT)aol.com)