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Search: id:A059403
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| 0, 0, 0, 1, 4, 9, 20, 36, 64, 100, 156, 225, 324, 441, 600, 784, 1024, 1296, 1640, 2025, 2500, 3025, 3660, 4356, 5184, 6084, 7140, 8281, 9604, 11025, 12656, 14400, 16384, 18496, 20880, 23409, 26244, 29241, 32580, 36100, 40000, 44100, 48620, 53361
(list; graph; listen)
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OFFSET
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0,5
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,500
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FORMULA
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a(n) =floor[floor[n^2/4]^2/4] =A002620(A002620(n))). a(4n)=4n^4; a(4n+1)=n^2*(2n+1)^2; a(4n+2)=2n(n+1)(2n(n+1)+1); a(4n+3)=(n+1)^2*(2n+1)^2. a(2n)=A060494(2n); a(2n-1)=A060494(2n-1)-A011861(n).
G.f.: x^3(1+2x+2x^3+x^4)/((1-x)^5*(1+x)^3*(1+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2008]
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EXAMPLE
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a(9)=100 since the ninth quarter-square is 20 and the twentieth quarter-square is 100.
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PROGRAM
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(PARI) { default(realprecision, 10); for (n = 0, 500, write("b059403.txt", n, " ", floor(floor(n^2/4)^2/4)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 26 2009]
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CROSSREFS
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Cf. A008233 for an alternative approach.
Sequence in context: A048150 A164931 A066186 this_sequence A009909 A009910 A060494
Adjacent sequences: A059400 A059401 A059402 this_sequence A059404 A059405 A059406
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 21 2001
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