A055607 a(2n+1) = n^2 - 1 + A002620(n), a(2n) = a(2n-1) + n.

0, 0, 2, 4, 7, 10, 14, 19, 24, 30, 36, 44, 51, 60, 68, 79, 88, 100, 110, 124, 135, 150, 162, 179, 192, 210, 224, 244, 259, 280, 296, 319, 336, 360, 378, 404, 423, 450, 470, 499, 520, 550, 572, 604, 627, 660, 684, 719, 744, 780, 806, 844, 871, 910, 938, 979, 1008

Offset

1,3

Comments

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.

References

Suggested by a chessboard problem from Antreas P. Hatzipolakis.

Links

Table of n, a(n) for n=1..57.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1).

Formula

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

Maple

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;

Crossrefs

Sequence in context: A127723 A076268 A323623 * A024512 A047808 A007980

Adjacent sequences: A055604 A055605 A055606 * A055608 A055609 A055610

Keyword

nonn,easy

Author

Len Smiley, Jun 02 2000

Extensions

More terms from Asher Auel

Status

approved