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a(2n+1) = n^2 - 1 + A002620(n), a(2n) = a(2n-1) + n.
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%I #15 Oct 27 2023 22:05:37

%S 0,0,2,4,7,10,14,19,24,30,36,44,51,60,68,79,88,100,110,124,135,150,

%T 162,179,192,210,224,244,259,280,296,319,336,360,378,404,423,450,470,

%U 499,520,550,572,604,627,660,684,719,744,780,806,844,871,910,938,979,1008

%N a(2n+1) = n^2 - 1 + A002620(n), a(2n) = a(2n-1) + n.

%C Consider an n X n chessboard. Place n queens in the cells of the first row, in cells (1,1), (2,1),..., (n,1) and [(n+1)/2] pawns in the odd cells of the second row, namely in cells (1,2), (3,2), (5,2), ... Sequence gives the number of cells that are not attacked by the queens.

%D Suggested by a chessboard problem from Antreas P. Hatzipolakis.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,1,-1,-1,1).

%F G.f. x^3(x^4 - x^3 - x^2 - 2x - 2)/((x-1)^3*(x+1)^2*(x^2+1)). - _Ralf Stephan_, Jul 25 2003

%p f := [0,0]: for i from 3 by 2 to 60 do f := [op(f),((i-1)/2)^2 - 1 + floor((i-1)/4)*ceil((i-1)/4)]: f := [op(f),f[nops(f)] + (i+1)/2]: od: f;

%K nonn,easy

%O 1,3

%A _Len Smiley_, Jun 02 2000

%E More terms from _Asher Auel_