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Search: id:A008794
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| 0, 0, 1, 1, 4, 4, 9, 9, 16, 16, 25, 25, 36, 36, 49, 49, 64, 64, 81, 81, 100, 100, 121, 121, 144, 144, 169, 169, 196, 196, 225, 225, 256, 256, 289, 289, 324, 324, 361, 361, 400, 400, 441, 441, 484, 484, 529, 529, 576, 576
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Also number of non-attacking kings on n-2 X n-2 board (cf. A030978). - Koksal Karakus (karakusk(AT)hotmail.com), May 27 2002
Maximum number of 2 X 2 tiles that fit on an n X n board. - Jon Perry (perry(AT)globalnet.co.uk), Aug 10 2003
(n)-(1) + (n-1) -(2) +(n-3)-(3)+ ... + (n-r) -(r)... n terms. e.g. 5-1+4-2+3=9 6-1+5-2+4-3=9 7-1+6-2+5-3+4 =16 8-1+7-2+6-3+5-4=16 - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 24 2005
The smallest possible number of white cells in a solution to an n X n nurikabe grid. [From Tanya Khovanova (tanyakh(AT)yahoo.com), Feb 24 2009]
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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a(n)=[floor(n/2)]^2
a(n)=(2n-1)(-1)^n/8+(2n^2-2n +1)/8; a(n+1)=sum{k=0..n, k(1-(-1)^k)/2}. - Paul Barry (pbarry(AT)wit.ie), May 31 2003
a(n)={sqrt[sum_{j=0..n}(j+1)*(cos(j*Pi)+1)/2]-1}^2 with n>=0. - Paolo P. Lava (ppl(AT)spl.at), Dec 04 2006
a(n+2) = SUM(A109613(k)*A059841(n-k): 0<=k<=n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 05 2009]
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MAPLE
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G.f.: x^2*(1+x^2)/((1-x^2)^2*(1-x)).
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CROSSREFS
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Cf. A086832.
Sequence in context: A014694 A065730 A145445 this_sequence A075709 A116682 A088190
Adjacent sequences: A008791 A008792 A008793 this_sequence A008795 A008796 A008797
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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