cp's OEIS Frontend

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.

A190579 Number of ways to place 6 nonattacking grasshoppers on an n x n chessboard.

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%I A190579 #15 Apr 04 2016 16:22:10
%S A190579 0,0,2,998,51618,873852,8039322,50272978,240764814,947860554,
%T A190579 3210392210,9649651136,26316155354,66191981440,155482089002,
%U A190579 344411086374,725043524246,1459722296638,2825136685698,5278863810724,9557560367842
%N A190579 Number of ways to place 6 nonattacking grasshoppers on an n x n chessboard.
%C A190579 The Grasshopper moves on the same lines as a queen, but must jump over a hurdle to land on the square immediately beyond.
%H A190579 Vincenzo Librandi, <a href="/A190579/b190579.txt">Table of n, a(n) for n = 1..1000</a>
%H A190579 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)
%F A190579 a(n) = n^12/720 -n^10/48 -5n^9/9 +509n^8/144 -187n^7/90 +701n^6/48 -14467n^5/36 +666917n^4/360 -471121n^3/180 -59875n^2/24 +57101n/6 -11339/2 -(9n^2/8-n-7/2)*(-1)^n, n>5.
%F A190579 G.f.: 2x^3*(8x^18 -59x^17 +110x^16 +71x^15 +473x^14 -3017x^13 -5401x^12 +23838x^11 -2727x^10 -119474x^9 -45545x^8 -20157x^7 -571677x^6 -1006961x^5 -689547x^4 -199704x^3 -20861x^2 -489x -1)/((x-1)^13*(x+1)^3).
%t A190579 CoefficientList[Series[2 x^2 (8 x^18 - 59 x^17 + 110 x^16 + 71 x^15 + 473 x^14 - 3017 x^13 - 5401 x^12 + 23838 x^11 - 2727 x^10 - 119474 x^9 - 45545 x^8 - 20157 x^7 - 571677 x^6 - 1006961 x^5 - 689547 x^4 - 199704 x^3 - 20861 x^2 - 489 x - 1) / ((x - 1)^13 (x + 1)^3), {x, 0, 50}], x] (* _Vincenzo Librandi_, Jun 03 2013 *)
%Y A190579 Cf. A190395, A190396, A190397, A176186, A190401.
%K A190579 nonn,easy
%O A190579 1,3
%A A190579 _Vaclav Kotesovec_, May 13 2011