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A274933 Maximal number of non-attacking queens on a quarter chessboard containing n^2 squares. 3
1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Take the quarter-board formed from a 2n-1 X 2n-1 chessboard by joining the center square to the top two corners. There are n^2 squares. If n = 11, 2n-1 = 21 and the board looks like this, with 11^2 = 121 squares (the top row is the top of the chessboard, the single cell at the bottom is at the center of the board):

OOOOOOOOOOOOOOOOOOOOO

-OOOOOOOOOOOOOOOOOOO-

--OOOOOOOOOOOOOOOOO--

---OOOOOOOOOOOOOOO---

----OOOOOOOOOOOOO----

-----OOOOOOOOOOO-----

------OOOOOOOOO------

-------OOOOOOO-------

--------OOOOO--------

---------OOO---------

----------O----------

The main question is, how does a(n) behave when n is large? (See A287866.)

This is a bisection of A287864. - Rob Pratt, Jun 04 2017

LINKS

Table of n, a(n) for n=1..45.

FORMULA

Since there can be at most one queen per row, a(n) <= n. In fact, since there cannot be a queen on both rows 1 and 2, a(n) <= n-1 for n>1. - N. J. A. Sloane, Jun 04 2017

EXAMPLE

For n=6 the maximal number is 5:

OOXOOOOOOOO

-OOOOOOXOO-

--OXOOOOO--

---OOOXO---

----OOO----

-----X-----

Examples from Rob Pratt, Jul 13 2016:

(i) For n=15 the maximal number is 13:

OOOOOOXOOOOOOOOOOOOOOOOOOOOOO

-OOOOOOOOOOOOOOOOOOXOOOOOOOO-

--OOOOOXOOOOOOOOOOOOOOOOOOO--

---OOOOOOOOOOOOOOOXOOOOOOO---

----OOOOOOOOOOOXOOOOOOOOO----

-----OOOOOOOXOOOOOOOOOOO-----

------OOOXOOOOOOOOOOOOO------

-------OOOOOOOOOXOOOOO-------

--------OOXOOOOOOOOOO--------

---------OOOOOOOOXOO---------

----------OOOOXOOOO----------

-----------XOOOOOO-----------

------------OXOOO------------

-------------OOO-------------

--------------O--------------

(ii) For n=31 the maximal number is 28:

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOO

-OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOO-

--OOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO--

---OOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO---

----OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOO----

-----OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOO-----

------OOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO------

-------OOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO-------

--------OOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOOO--------

---------OOOOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOO---------

----------OOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOOO----------

-----------OOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOOOOO-----------

------------OOOOOOOOOOOOOOOOOOOOOOOOOOOXOOOOOOOOO------------

-------------OOOOOOOOOOOOOOOOOOXOOOOOOOOOOOOOOOO-------------

--------------OOOOOOOOOOXOOOOOOOOOOOOOOOOOOOOOO--------------

---------------OOOOOXOOOOOOOOOOOOOOOOOOOOOOOOO---------------

----------------OOOOOOOXOOOOOOOOOOOOOOOOOOOOO----------------

-----------------OOOOOOOOOOOOOOOOOOOXOOOOOOO-----------------

------------------OOOOXOOOOOOOOOOOOOOOOOOOO------------------

-------------------OOOOOOOOOOOOOOOOXOOOOOO-------------------

--------------------OXOOOOOOOOOOOOOOOOOOO--------------------

---------------------OOOOOOOOOOOOOXOOOOO---------------------

----------------------OOOOOOOOXOOOOOOOO----------------------

-----------------------OOOXOOOOOOOOOOO-----------------------

------------------------OOOOOOOOOXOOO------------------------

-------------------------XOOOOOOOOOO-------------------------

--------------------------OOOOOOXOO--------------------------

---------------------------OOXOOOO---------------------------

----------------------------OOOOO----------------------------

-----------------------------OOO-----------------------------

------------------------------O------------------------------

CROSSREFS

Cf. A274616, A287864, A287866.

Sequence in context: A291041 A291766 A291579 * A080331 A297247 A167463

Adjacent sequences:  A274930 A274931 A274932 * A274934 A274935 A274936

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Jul 13 2016

EXTENSIONS

Terms a(n) with n >= 15 corrected and extended by Rob Pratt, Jul 13 2016

STATUS

approved

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Last modified December 12 07:31 EST 2019. Contains 329948 sequences. (Running on oeis4.)