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

Author

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

Keywords

• nonn
• nice
• easy

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).

Crossrefs

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

Programs

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 *)

PARI

Vec(x^2*(x^2-2*x+3)/(x-1)^2 + O(x^100)) \\ Colin Barker, Nov 08 2014

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

Extensions

More terms from Jud McCranie, Aug 11 2001