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.

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.

Links

Colin Barker, Table of n, a(n) for n = 2..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1).

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

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

Sequence in context: A173472 A334905 A058992 * A092535 A215476 A204662

Adjacent sequences: A051752 A051753 A051754 * A051756 A051757 A051758

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