A035289 Number of ways to place a non-attacking white and black knight on n X n chessboard.

0, 12, 56, 192, 504, 1100, 2112, 3696, 6032, 9324, 13800, 19712, 27336, 36972, 48944, 63600, 81312, 102476, 127512, 156864, 191000, 230412, 275616, 327152, 385584, 451500, 525512, 608256, 700392, 802604, 915600, 1040112, 1176896

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = n^4 - 9 n^2 + 24 n - 16.

G.f.: 4*x^2*(4*x^3-8*x^2+x-3)/(x-1)^5. [Colin Barker, Jan 09 2013]

Example

There are 56 ways of putting 2 distinct knights on 3 X 3 so that neither can capture the other

Mathematica

CoefficientList[Series[4 x (4 x^3 - 8 x^2 + x - 3)/(x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 20 2013 *)

Prog

(Magma) [n^4 - 9*n^2 + 24*n - 16: n in [1..50]]; // Vincenzo Librandi, Oct 20 2013

Crossrefs

Sequence in context: A331771 A009430 A348584 * A275505 A009827 A068418

Adjacent sequences: A035286 A035287 A035288 * A035290 A035291 A035292

Keyword

nonn,easy

Author

Erich Friedman

Status

approved