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
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
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