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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
3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130
OFFSET
2,1
COMMENTS
3 followed by the positive even integers starting with 4. - Wesley Ivan Hurt, Feb 09 2014
REFERENCES
Peter Hayes, A Problem of Chess Queens, Journal of Recreational Mathematics, 24(4), 1992, 264-271.
FORMULA
a(2) = 3, a(n) = 2n-2 for n >= 3.
a(n) = 2*a(n-1)-a(n-2) for n>4. - Colin Barker, Nov 08 2014
G.f.: x^2*(x^2-2*x+3) / (x-1)^2. - Colin Barker, Nov 08 2014
MAPLE
A051755:=n->`if`(n=2, 3, 2*n-2); seq(A051755(n), n=2..50); # Wesley Ivan Hurt, Feb 09 2014
MATHEMATICA
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 *)
LinearRecurrence[{2, -1}, {3, 4, 6}, 70] (* Harvey P. Dale, Aug 29 2017 *)
PROG
(PARI) Vec(x^2*(x^2-2*x+3)/(x-1)^2 + O(x^100)) \\ Colin Barker, Nov 08 2014
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Robert Trent (trentrd(AT)hotmail.com), Aug 23 2000
EXTENSIONS
More terms from Jud McCranie, Aug 11 2001
STATUS
approved