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.

A061991 Number of ways to place 5 nonattacking queens on a 5 X n board.

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%I A061991 #11 Apr 23 2023 22:26:57
%S A061991 0,0,0,0,0,10,40,164,568,1614,3916,8492,16852,31100,54068,89428,
%T A061991 141812,216932,321700,464348,654548,903532,1224212,1631300,2141428,
%U A061991 2773268,3547652,4487692,5618900,6969308,8569588,10453172,12656372,15218500,18181988,21592508
%N A061991 Number of ways to place 5 nonattacking queens on a 5 X n board.
%H A061991 Vincenzo Librandi, <a href="/A061991/b061991.txt">Table of n, a(n) for n = 0..1000</a>
%H A061991 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Ways of placing non-attacking queens and kings...</a>, part of "Between chessboard and computer", 1996, pp. 204 - 206.
%H A061991 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A061991 G.f.: 2*x^5*(4*x^11 - 11*x^10 + 16*x^9 + 7*x^8 - 32*x^7 + 38*x^6 + 6*x^5 + 8*x^4 - 8*x^3 + 37*x^2 - 10*x + 5)/(x - 1)^6.
%F A061991 Recurrence: a(n) = 6*a(n - 1) - 15*a(n - 2) + 20*a(n - 3) - 15*a(n - 4) + 6*a(n - 5) - a(n - 6), n >= 17.
%F A061991 Explicit formula (V. Kotesovec, 1992): a(n) = n^5 - 30*n^4 + 407*n^3 - 3098*n^2 + 13104*n - 24332, n >= 11.
%t A061991 CoefficientList[Series[2 x^5 (4 x^11 -11 x^10 + 16 x^9 + 7 x^8 - 32 x^7 + 38 x^6 + 6 x^5 + 8 x^4 - 8 x^3 + 37 x^2 - 10 x + 5) / (x-1)^6, {x, 0, 30}], x] (* _Vincenzo Librandi_, May 12 2013 *)
%Y A061991 Cf. A061989, A061990.
%K A061991 nonn,easy
%O A061991 0,6
%A A061991 Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 31 2001