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A309779
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Squares that can be expressed as the sum of two positive squares but not as the sum of three positive squares.
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2
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25, 100, 400, 1600, 6400, 25600, 102400, 409600, 1638400, 6553600, 26214400, 104857600, 419430400, 1677721600, 6710886400, 26843545600, 107374182400, 429496729600, 1717986918400, 6871947673600, 27487790694400, 109951162777600, 439804651110400, 1759218604441600
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OFFSET
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1,1
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COMMENTS
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This sequence comes from the study of A309778, exactly, A309778(n) = 2 iff n^2 belongs to this sequence here.
According to Draxl link, a(n) is a term of this sequence iff a(n) = 5^2 * 4^(n-1) with n >= 1.
This sequence is a subsequence of A219222 whose terms are all of the form b_0 * 4^k with b_0 in A051952, hence, the only primitive term of this sequence here is 25.
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LINKS
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FORMULA
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a(n) = 5^2 * 4^(n-1) with n >= 1.
a(n) = 4*a(n-1) for n > 1. G.f.: 25*x/(1 - 4*x). - Chai Wah Wu, Aug 29 2019
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EXAMPLE
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25 = 5^2 = 3^2 + 4^2,
100 = 10^2 = 6^2 + 8^2,
5^2 * 4^(n-1) = (5 * 2^(n-1))^2 = (3 * 2^(n-1))^2 + (4 * 2^(n-1))^2, but these terms are not the sum of three positive squares.
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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