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A035288 Number of ways to place a non-attacking white and black bishop on n X n chessboard. 2
0, 8, 52, 184, 480, 1040, 1988, 3472, 5664, 8760, 12980, 18568, 25792, 34944, 46340, 60320, 77248, 97512, 121524, 149720, 182560, 220528, 264132, 313904, 370400, 434200, 505908, 586152, 675584, 774880, 884740, 1005888, 1139072, 1285064 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = 2 * A172123(n). [Vaclav Kotesovec, Nov 28 2011]

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) = (3 n^4 - 4 n^3 + 3 n^2 - 2 n)/3.

a(1)=0, a(2)=8, a(3)=52, a(4)=184, a(5)=480, a(n) = 5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5). [Harvey P. Dale, Nov 19 2011]

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

EXAMPLE

There are 52 ways of putting 2 distinct bishops on 3 X 3 so that neither can capture the other

MATHEMATICA

Table[(3n^4-4n^3+3n^2-2n)/3, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {0, 8, 52, 184, 480}, 40] (* Harvey P. Dale, Nov 19 2011 *)

PROG

(MAGMA) [(3*n^4-4*n^3+3*n^2-2*n)/3: n in [1..35]]; // Vincenzo Librandi, May 04 2013

(PARI) a(n)=(3*n^4-4*n^3+3*n^2-2*n)/3; \\ Joerg Arndt, May 04 2013

CROSSREFS

Sequence in context: A180319 A199706 A302318 * A303012 A024179 A302816

Adjacent sequences:  A035285 A035286 A035287 * A035289 A035290 A035291

KEYWORD

nonn,easy

AUTHOR

Erich Friedman

STATUS

approved

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Last modified December 16 14:52 EST 2018. Contains 318167 sequences. (Running on oeis4.)