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A202655 Number of ways to place 4 nonattacking semi-queens on an n X n board. 5
0, 0, 0, 7, 223, 2429, 15045, 66122, 230074, 675798, 1745318, 4073993, 8764753, 17630795, 33522531, 60756612, 105666148, 177293340, 288246972, 455749371, 702898611, 1060173961, 1567213681, 2274896558, 3247759614, 4566786770, 6332604226, 8669120733, 11727651845 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.

V. Kotesovec, Non-attacking chess pieces

FORMULA

a(n) = n^8/24 - 2*n^7/3 + 41*n^6/9 - 257*n^5/15 + 341*n^4/9 - 97*n^3/2 + 2341*n^2/72 - 87*n/10 + (n/2 - 1/2)*floor(n/2).

G.f.: -x^4*(151*x^6 + 1022*x^5 + 2233*x^4 + 2132*x^3 + 1001*x^2 + 174*x + 7)/((x-1)^9*(x+1)^2).

MATHEMATICA

Rest@ CoefficientList[Series[-x^4*(151 x^6 + 1022 x^5 + 2233 x^4 + 2132 x^3 + 1001 x^2 + 174 x + 7)/((x - 1)^9*(x + 1)^2), {x, 0, 29}], x] (* Michael De Vlieger, Aug 19 2019 *)

CROSSREFS

Cf. A099152, A061994, A103220, A202654, A202656, A202657.

Sequence in context: A231488 A231487 A140018 * A009488 A302059 A352312

Adjacent sequences:  A202652 A202653 A202654 * A202656 A202657 A202658

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 22 2011

STATUS

approved

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Last modified June 24 21:51 EDT 2022. Contains 354830 sequences. (Running on oeis4.)