A374933 Maximum number of squares covered (i.e., attacked) by 2 independent (i.e., non-attacking) queens on an n X n chessboard.

9, 15, 23, 30, 37, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388, 396, 404, 412, 420

Offset

3,1

Comments

It is not possible to place two non-attacking queens on a 1 X 1 or 2 X 2 chessboard.

Links

Paolo Xausa, Table of n, a(n) for n = 3..10000

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

Formula

a(n) = 8*n - 20 for n >= 8.

G.f.: x^3*(9 - 3*x + 2*x^2 - x^3 + x^6)/(1 - x)^2. - Stefano Spezia, Jul 25 2024

Mathematica

LinearRecurrence[{2, -1}, {9, 15, 23, 30, 37, 44, 52}, 60] (* Paolo Xausa, Jan 19 2026 *)

Crossrefs

Cf. A017113, A047461 (case for one queen).

Sequence in context: A102739 A124622 A189051 * A274288 A172292 A075638

Adjacent sequences: A374930 A374931 A374932 * A374934 A374935 A374936

Keyword

nonn,easy

Author

John King, Jul 24 2024

Status

approved