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A035286 Number of ways to place a non-attacking 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 (list; graph; refs; listen; history; text; internal format)
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+x-8)/(x-1)^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

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Last modified December 14 19:52 EST 2018. Contains 318116 sequences. (Running on oeis4.)