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A051755 Consider problem of placing N queens on an n X n board so that each queen attacks precisely 2 others. Sequence gives maximal number of queens. 10

%I #22 Aug 29 2017 14:50:15

%S 3,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,

%T 50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,

%U 96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130

%N Consider problem of placing N queens on an n X n board so that each queen attacks precisely 2 others. Sequence gives maximal number of queens.

%C 3 followed by the positive even integers starting with 4. - _Wesley Ivan Hurt_, Feb 09 2014

%D Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.

%H Colin Barker, <a href="/A051755/b051755.txt">Table of n, a(n) for n = 2..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(2) = 3, a(n) = 2n-2 for n >= 3.

%F a(n) = 2*a(n-1)-a(n-2) for n>4. - _Colin Barker_, Nov 08 2014

%F G.f.: x^2*(x^2-2*x+3) / (x-1)^2. - _Colin Barker_, Nov 08 2014

%p A051755:=n->`if`(n=2, 3, 2*n-2); seq(A051755(n), n=2..50); # _Wesley Ivan Hurt_, Feb 09 2014

%t CoefficientList[Series[(z^2 - 2*z + 3)/(z - 1)^2, {z, 0, 100}], z] (* and *) Join[{3}, Table[2*n, {n, 2, 200}]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 10 2011 *)

%t LinearRecurrence[{2,-1},{3,4,6},70] (* _Harvey P. Dale_, Aug 29 2017 *)

%o (PARI) Vec(x^2*(x^2-2*x+3)/(x-1)^2 + O(x^100)) \\ _Colin Barker_, Nov 08 2014

%Y Cf. A051754-A051759, A051567-A051571, A019654.

%K nonn,nice,easy

%O 2,1

%A Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000

%E More terms from _Jud McCranie_, Aug 11 2001

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)