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 A202657 #12 Aug 23 2024 12:16:53
%S A202657 0,0,0,0,0,83,6107,126376,1377328,9984758,54399330,239675936,
%T A202657 895773148,2935757573,8641608781,23259768860,58039719112,135720432200,
%U A202657 299995484600,631220344328,1271607596876,2464466665667,4613731163831,8372196591052,14769606793684,25395151577010
%N A202657 Number of ways to place 6 nonattacking semi-queens on an n X n board.
%C A202657 Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.
%H A202657 Michael De Vlieger, <a href="/A202657/b202657.txt">Table of n, a(n) for n = 1..10000</a>
%H A202657 Christopher R. H. Hanusa, Thomas Zaslavsky, <a href="https://arxiv.org/abs/1906.08981">A q-queens problem. VII. Combinatorial types of nonattacking chess riders</a>, arXiv:1906.08981 [math.CO], 2019.
%H A202657 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>
%H A202657 <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (5, -4, -18, 30, 24, -61, -31, 74, 70, -92, -104, 104, 92, -70, -74, 31, 61, -24, -30, 18, 4, -5, 1).
%F A202657 a(n) = n^12/720 - n^11/18 + 73*n^10/72 - 72247*n^9/6480 + 5909*n^8/72 - 320653*n^7/756 + 112795*n^6/72 - 8892919*n^5/2160 + 8086231*n^4/1080 - 5740271*n^3/648 + 2598425*n^2/432 - 13161367*n/7560 + (n^5/4 - 77*n^4/12 + 757*n^3/12 - 7007*n^2/24 + 14581*n/24 - 1677/4)*floor(n/2) + (64*n/9 - 88/9)*floor(n/3) + (8*n/3 - 52/9)*floor((n + 1)/3).
%F A202657 G.f.: -x^6*(31709*x^16 + 377288*x^15 + 2265487*x^14 + 8441426*x^13 + 22166758*x^12 + 43217858*x^11 + 64805639*x^10 + 75943200*x^9 + 70077016*x^8 + 50738668*x^7 + 28477437*x^6 + 12074418*x^5 + 3711058*x^4 + 771370*x^3 + 96173*x^2 + 5692*x + 83)/((x-1)^13*(x+1)^6*(x^2+x+1)^2).
%t A202657 Rest@ CoefficientList[Series[-x^6*(31709 x^16 + 377288 x^15 + 2265487 x^14 + 8441426 x^13 + 22166758 x^12 + 43217858 x^11 + 64805639 x^10 + 75943200 x^9 + 70077016 x^8 + 50738668 x^7 + 28477437 x^6 + 12074418 x^5 + 3711058 x^4 + 771370 x^3 + 96173 x^2 + 5692 x + 83)/((x - 1)^13*(x + 1)^6*(x^2 + x + 1)^2), {x, 0, 26}], x] (* _Michael De Vlieger_, Aug 19 2019 *)
%Y A202657 Cf. A099152, A176186, A103220, A202654, A202655, A202656.
%K A202657 nonn
%O A202657 1,6
%A A202657 _Vaclav Kotesovec_, Dec 22 2011