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A195658
Number of ways to place 9n nonattacking kings on a vertical cylinder 18 X 2n.
2
1024, 50922, 815816, 7238864, 44693472, 216134044, 877751236, 3130270224, 10105541204, 30179587994, 84719304384, 226268016376, 580363147336, 1440139184616, 3477556916828, 8210011147304, 19021962952188, 43385173057846, 97653259485592, 217359166880016
OFFSET
1,1
COMMENTS
Vertical cylinder: a chessboard where it is supposed that the columns 1 and 18 are in contact (number of columns = 18, number of rows = 2n)
LINKS
Index entries for linear recurrences with constant coefficients, signature (12, -64, 200, -406, 560, -532, 344, -145, 36, -4).
FORMULA
Recurrence: a(n) = -4*a(n-10) + 36*a(n-9) - 145*a(n-8) + 344*a(n-7) - 532*a(n-6) + 560*a(n-5) - 406*a(n-4) + 200*a(n-3) - 64*a(n-2) + 12*a(n-1).
G.f.: (1 + 1012*x + 38698*x^2 + 270088*x^3 + 503686*x^4 + 270112*x^5 + 37900*x^6 + 1516*x^7 + 25*x^8)/((x-1)^8*(2*x-1)^2).
a(n) = (21623809*n - 226349399)*2^n + 8913/40*n^7 + 124781/20*n^6 + 376359/4*n^5 + 977074*n^4 + 294753537/40*n^3 + 787733819/20*n^2 + 135269649*n + 226349400.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 22 2011
STATUS
approved