A195591 Number of ways to place 3n nonattacking kings on a vertical cylinder 6 X 2n.

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).

Links

Ray Chandler, Table of n, a(n) for n = 1..3305

V. Kotesovec, Non-attacking chess pieces

Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4).

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

Cf. A194645, A061594, A137432.

Sequence in context: A119771 A055920 A055856 * A240292 A050406 A047674

Adjacent sequences: A195588 A195589 A195590 * A195592 A195593 A195594

Keyword

nonn

Author

Vaclav Kotesovec, Sep 21 2011

Status

approved