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 A172213 #15 Jun 26 2025 11:53:07
%S A172213 1,16,84,412,1416,3640,7928,15384,27352,45432,71480,107608,156184,
%T A172213 219832,301432,404120,531288,686584,873912,1097432,1361560,1670968,
%U A172213 2030584,2445592,2921432
%N A172213 Number of ways to place 4 nonattacking knights on a 4 X n board.
%H A172213 Vincenzo Librandi, <a href="/A172213/b172213.txt">Table of n, a(n) for n = 1..1000</a>
%H A172213 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a>
%H A172213 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A172213 Explicit formula (Vaclav Kotesovec, 26.1.2010): a(n) = 8*(4*n^4-36*n^3+170*n^2-450*n+537)/3, n>=6.
%F A172213 G.f.: -x*(16*x^9-20*x^8-40*x^7+172*x^6-81*x^5+41*x^4+142*x^3+14*x^2+11*x+1)/(x-1)^5. - _Vaclav Kotesovec_, Mar 25 2010
%F A172213 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Wesley Ivan Hurt_, Jun 26 2025
%t A172213 CoefficientList[Series[-(16 x^9 - 20 x^8 - 40 x^7 + 172 x^6 - 81 x^5 + 41 x^4 + 142 x^3 + 14 x^2 + 11 x + 1) / (x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 27 2013 *)
%t A172213 LinearRecurrence[{5,-10,10,-5,1},{1,16,84,412,1416,3640,7928,15384,27352,45432},30] (* _Harvey P. Dale_, Apr 16 2022 *)
%Y A172213 Cf. A172135, A061990, A172212.
%K A172213 nonn,easy
%O A172213 1,2
%A A172213 _Vaclav Kotesovec_, Jan 29 2010