cp's OEIS Frontend

A035290 Number of ways to place a non-attacking white and black pawn on n X n chessboard.

%I A035290 #18 Sep 08 2022 08:44:52
%S A035290 0,0,6,50,194,522,1142,2186,3810,6194,9542,14082,20066,27770,37494,
%T A035290 49562,64322,82146,103430,128594,158082,192362,231926,277290,328994,
%U A035290 387602,453702,527906,610850,703194,805622,918842,1043586,1180610
%N A035290 Number of ways to place a non-attacking white and black pawn on n X n chessboard.
%H A035290 Vincenzo Librandi, <a href="/A035290/b035290.txt">Table of n, a(n) for n = 1..1000</a>
%H A035290 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A035290 a(n) = n^4 - 4 n^3 + n^2 + 10 n - 6.
%F A035290 G.f.: -2*x^3*(x+1)*(x^3-5*x^2+7*x+3)/(x-1)^5. [_Colin Barker_, Jan 09 2013]
%e A035290 There are 6 ways of putting 1 white and 1 black pawn on 3 X 3 so that neither can capture the other. pawns can't be on first or last rank.
%t A035290 CoefficientList[Series[- 2 x^2 (x + 1) (x^3 - 5 x^2 + 7 x + 3)/(x - 1)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 20 2013 *)
%o A035290 (Magma) [n le 2 select 0 else n^4-4*n^3+n^2+10*n-6: n in [1..50]]; // _Vincenzo Librandi_, Oct 20 2013
%K A035290 nonn,easy
%O A035290 1,3
%A A035290 _Erich Friedman_