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A030179
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Quarter-squares squared: A002620^2.
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3
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0, 0, 1, 4, 16, 36, 81, 144, 256, 400, 625, 900, 1296, 1764, 2401, 3136, 4096, 5184, 6561, 8100, 10000, 12100, 14641, 17424, 20736, 24336, 28561, 33124, 38416, 44100, 50625, 57600, 65536, 73984, 83521, 93636, 104976, 116964
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Conjectured to be crossing number of complete bipartite graph K_{n,n}. Known to be true for n <= 7.
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REFERENCES
| C. Thomassen, Embeddings and minors, pp. 301-349 of R. L. Graham et al., eds., Handbook of Combinatorics, MIT Press.
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LINKS
| G. Xiao, Contfrac
E. Weisstein, Zarankiewicz's Conjecture.html
Index to sequences with linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2010]
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FORMULA
| Floor(n^2/4)^2.
G.f.: x^2*(1+2*x+6*x^2+2*x^3+x^4) / ( (1+x)^3*(1-x)^5 ). a(n) = +2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2010]
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MATHEMATICA
| f[n_]:=Floor[n^2/2]; Table[Nest[f, n, 2], {n, 5!}]/2 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 10 2010]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {0, 0, 1, 4, 16, 36, 81, 144}, 6] (* From Harvey P. Dale, Apr 26 2011 *)
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CROSSREFS
| C. A000241, A002620, A014540.
Sequence in context: A063755 A166721 A085040 * A189145 A005722 A075408
Adjacent sequences: A030176 A030177 A030178 * A030180 A030181 A030182
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 10 2002
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