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A195591
Number of ways to place 3n nonattacking kings on a vertical cylinder 6 X 2n.
2
16, 90, 344, 1082, 3036, 7918, 19648, 47058, 109796, 251126, 565512, 1257754, 2769196, 6046014, 13107536, 28246370, 60555636, 129237382, 274727320, 581960106, 1228931516, 2587886030, 5435818464, 11391730162, 23823647236, 49727668758, 103616086568
OFFSET
1,1
COMMENTS
Vertical cylinder: a chessboard where it is supposed that the columns 1 and 6 are in contact (number of columns = 6, number of rows = 2n).
FORMULA
Recurrence: a(n) = -4*a(n-4) + 12*a(n-3) - 13*a(n-2) + 6*a(n-1).
G.f.: (1+10*x+7*x^2)/((x-1)^2*(2*x-1)^2).
a(n) = (31*n - 65)*2^n + 18*n + 66.
MATHEMATICA
LinearRecurrence[{6, -13, 12, -4}, {16, 90, 344, 1082}, 30] (* Harvey P. Dale, Nov 15 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 21 2011
STATUS
approved