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A035288 Number of ways to place a non-attacking white and black bishop on n X n chessboard. 2

%I

%S 0,8,52,184,480,1040,1988,3472,5664,8760,12980,18568,25792,34944,

%T 46340,60320,77248,97512,121524,149720,182560,220528,264132,313904,

%U 370400,434200,505908,586152,675584,774880,884740,1005888,1139072,1285064

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

%C a(n) = 2 * A172123(n). [_Vaclav Kotesovec_, Nov 28 2011]

%H Vincenzo Librandi, <a href="/A035288/b035288.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

%F 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]

%F G.f.: -4*x^2*(x+1)*(x+2)/(x-1)^5. [_Colin Barker_, Jan 09 2013]

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

%t 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 *)

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

%o (PARI) a(n)=(3*n^4-4*n^3+3*n^2-2*n)/3; \\ _Joerg Arndt_, May 04 2013

%K nonn,easy

%O 1,2

%A _Erich Friedman_

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Last modified June 26 10:12 EDT 2019. Contains 324375 sequences. (Running on oeis4.)