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A059403
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Quarter-squared applied twice.
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2
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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;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 2, 0, -2, 4, -1, -2, 1).
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FORMULA
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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.
G.f.: x^3(1+2x+2x^3+x^4)/((1-x)^5*(1+x)^3*(1+x^2)). [R. J. Mathar, 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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MATHEMATICA
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Floor[Floor[Range[0, 50]^2/4]^2/4] (* or *) LinearRecurrence[{2, 1, -4, 2, 0, -2, 4, -1, -2, 1}, {0, 0, 0, 1, 4, 9, 20, 36, 64, 100}, 50] (* Harvey P. Dale, Dec 13 2014 *)
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PROG
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(PARI) { default(realprecision, 10); for (n = 0, 500, write("b059403.txt", n, " ", floor(floor(n^2/4)^2/4)); ) } \\ Harry J. Smith, Jun 26 2009
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CROSSREFS
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Cf. A008233 for an alternative approach.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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