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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
OFFSET
1,4
COMMENTS
Two semi-queens do not attack each other if they are in the same northwest-southeast diagonal.
LINKS
Christopher R. H. Hanusa, Thomas Zaslavsky, A q-queens problem. VII. Combinatorial types of nonattacking chess riders, arXiv:1906.08981 [math.CO], 2019.
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
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Dec 22 2011
STATUS
approved