

A035286


Number of ways to place a nonattacking white and black king on n X n chessboard.


1



0, 0, 32, 156, 456, 1040, 2040, 3612, 5936, 9216, 13680, 19580, 27192, 36816, 48776, 63420, 81120, 102272, 127296, 156636, 190760, 230160, 275352, 326876, 385296, 451200, 525200, 607932, 700056, 802256, 915240, 1039740, 1176512, 1326336
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OFFSET

1,3


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 + 12 n  4.
G.f.: 4*x^3*(x^2+x8)/(x1)^5. [Colin Barker, Jan 09 2013]


EXAMPLE

There are 32 ways of putting 2 distinct kings on 3 X 3 so that neither can capture the other


MATHEMATICA

CoefficientList[Series[4 x^2 (x^2 + x  8)/(x  1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 20 2013 *)


PROG

(MAGMA) [n^4  9*n^2 + 12*n  4: n in [1..40]]; // Vincenzo Librandi, Oct 20 2013


CROSSREFS

Sequence in context: A126419 A197621 A318159 * A298219 A299348 A299095
Adjacent sequences: A035283 A035284 A035285 * A035287 A035288 A035289


KEYWORD

nonn,easy


AUTHOR

Erich Friedman


STATUS

approved



