

A195593


Number of ways to place 5n nonattacking kings on a vertical cylinder 10 X 2n.


2



64, 732, 4392, 18890, 66532, 205628, 580664, 1536814, 3877300, 9434784, 22327496, 51698178, 117645348, 263992580, 585640568, 1286898262, 2805399156, 6074441896, 13076687560, 28009586346, 59732295204, 126891641612, 268638308152, 566987715710
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OFFSET

1,1


COMMENTS

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 10 are in contact (number of columns = 10, number of rows = 2n).


LINKS



FORMULA

a(n) = 4*a(n6) + 20*a(n5)  41*a(n4) + 44*a(n3)  26*a(n2) + 8*a(n1).
G.f.: (1 + 56*x + 246*x^2 + 156*x^3 + 11*x^4)/((x1)^4*(2*x1)^2).
a(n) = (1771*n  8709)*2^n + 235/3*n^3 + 880*n^2 + 12815/3*n + 8710.


MATHEMATICA

LinearRecurrence[{8, 26, 44, 41, 20, 4}, {64, 732, 4392, 18890, 66532, 205628}, 20] (* Jinyuan Wang, Feb 26 2020 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



