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 A075561 #51 Feb 16 2025 08:32:47
%S A075561 1,1,1,4,4,4,9,9,9,16,16,16,25,25,25,36,36,36,49,49,49,64,64,64,81,81,
%T A075561 81,100,100,100,121,121,121,144,144,144,169,169,169,196,196,196,225,
%U A075561 225,225,256,256,256,289,289,289,324,324,324,361,361,361,400,400
%N A075561 Domination number for kings' graph K(n).
%C A075561 Also the lower independence number of the n X n knight graph. - _Eric W. Weisstein_, Aug 01 2023
%D A075561 John J. Watkins, Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, 2004, p. 102.
%H A075561 Vincenzo Librandi, <a href="/A075561/b075561.txt">Table of n, a(n) for n = 1..1000</a>
%H A075561 Irene Choi, Shreyas Ekanathan, Aidan Gao, Tanya Khovanova, Sylvia Zia Lee, Rajarshi Mandal, Vaibhav Rastogi, Daniel Sheffield, Michael Yang, Angela Zhao, and Corey Zhao, <a href="https://arxiv.org/abs/2212.01468">The Struggles of Chessland</a>, arXiv:2212.01468 [math.HO], 2022.
%H A075561 Matthew D. Kearse and Peter B. Gibbons, <a href="http://www.cs.auckland.ac.nz/research/groups/CDMTCS/researchreports/133chess.pdf">Computational Methods and New Results for Chessboard Problems</a>, Centre for Discrete Mathematics and Theoretical Computer Science, CDMTCS-133, May 2000.
%H A075561 Matthew D. Kearse and Peter B. Gibbons, <a href="http://ajc.maths.uq.edu.au/pdf/23/ocr-ajc-v23-p253.pdf">Computational Methods and New Results for Chessboard Problems</a>, Australasian Journal of Combinatorics 23 (2001), 253-284.
%H A075561 Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], 2024. See p. 15.
%H A075561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%H A075561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingGraph.html">King Graph</a>
%H A075561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KingsProblem.html">Kings Problem</a>
%H A075561 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LowerIndependenceNumber.html">Lower Independence Number</a>
%H A075561 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F A075561 a(n) = floor((n+2)/3)^2. - _Vaclav Kotesovec_, May 13 2012
%F A075561 G.f.: -x*(x+1)*(x^2-x+1) / ((x-1)^3*(x^2+x+1)^2). - _Colin Barker_, Oct 06 2014
%F A075561 E.g.f.: exp(-x/2)*(exp(3*x/2)*(5 + 3*x*(3 + x)) + (6*x - 5)*cos(sqrt(3)*x/2) + sqrt(3)*(3 + 2*x)*sin(sqrt(3)*x/2))/27. - _Stefano Spezia_, Oct 17 2022
%F A075561 Sum_{n>=1} 1/a(n) = Pi^2/2 (A102753). - _Amiram Eldar_, Nov 03 2022
%t A075561 Table[Floor[(n + 2)/3]^2, {n, 50}] (* _Vaclav Kotesovec_, May 13 2012 *)
%t A075561 LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 1, 1, 4, 4, 4, 9}, 20] (* _Eric W. Weisstein_, Jun 20 2017 *)
%t A075561 CoefficientList[Series[(-1 - x^3)/((-1 + x)^3 (1 + x + x^2)^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jun 20 2017 *)
%o A075561 (PARI) Vec(-x*(x+1)*(x^2-x+1)/((x-1)^3*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Oct 06 2014
%Y A075561 Cf. A189889, A075458, A006075, A102753.
%K A075561 nonn,easy
%O A075561 1,4
%A A075561 _N. J. A. Sloane_, Oct 16 2002
%E A075561 More terms added from _Vaclav Kotesovec_, May 13 2012