A035288 Number of ways to place a non-attacking white and black bishop on n X n chessboard.

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

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

Cf. A172123.

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