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 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; text; 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), ... 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

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Last modified April 18 11:52 EDT 2024. Contains 371779 sequences. (Running on oeis4.)