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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. 9
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 (list; graph; refs; listen; history; text; internal format)
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: A184736 A173472 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

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Last modified June 19 10:32 EDT 2019. Contains 324219 sequences. (Running on oeis4.)