|
| |
|
|
A055607
|
|
a(2n+1) = n^2 - 1 + A002620(n), a(2n) = a(2n-1) + n.
|
|
0
| |
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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), ... Which is the number of the unattacked (by the queens) cells ? How many cells are not attacked by the queens?
|
|
|
REFERENCES
| Suggested by a chess-board problem from Antreas P. Hatzipolakis.
|
|
|
FORMULA
| G.f. x^3(x^4-x^3-x^2-2x-2)/(x-1)^3/(x+1)^2/(x^2+1). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 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: A145106 A127723 A076268 * A024512 A047808 A007980
Adjacent sequences: A055604 A055605 A055606 * A055608 A055609 A055610
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Leonard Smiley (smiley(AT)math.uaa.alaska.edu), Jun 02 2000
|
|
|
EXTENSIONS
| More terms from Asher Natan Auel (auela(AT)reed.edu)
|
| |
|
|
