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A241924
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16*s^8 - 168*s^4*t^4 + 9*t^8, where s > 0, t = 1..s.
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3
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-143, 1417, -36608, 91377, -110448, -938223, 1005577, 362752, -2376023, -9371648, 6145009, 4572304, -2195951, -20040176, -55859375, 26656137, 23392512, 9296937, -28274688, -105690519, -240185088, 91833457, 85785232, 59623057, -10435568, -156352559
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listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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Sequence lists, in nonincreasing order, the y-values in special solutions to x^4 + y^3 = z^2, that is: A241923(n)^4 + a(n)^3 = A241925(n)^2 (see also Cohen's post in Links section).
Note that 16*s^8 - 168*s^4*t^4 + 9*t^8 = (4*s^4 - 12*s^2*t^2 - 3*t^4)*(4s^4 + 12*s^2*t^2 - 3*t^4).
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
D. Alpern, List of first 1602 solutions to a^4 + b^3 = c^2 for increasing values of a, where gcd(a,b,c) = 1.
D. Alpern, Sum of powers, a^4 + b^3 = c^2.
Henri Cohen, a^m + b^n = c^p (was: Sum of two powers = Square), post in the newsgroup sci.math.research, Jan 09 1998.
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MATHEMATICA
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Flatten[Table[16 s^8 - 168 s^4 t^4 + 9 t^8, {s, 10}, {t, s}]]
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PROG
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(MAGMA) [16*s^8-168*s^4*t^4+9*t^8: t in [1..s], s in [1..10]];
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CROSSREFS
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Cf. A096741, A241923, A241925.
Sequence in context: A074301 A156635 A035304 * A185514 A220292 A159054
Adjacent sequences: A241921 A241922 A241923 * A241925 A241926 A241927
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KEYWORD
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sign
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AUTHOR
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Vincenzo Librandi, May 02 2014
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STATUS
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approved
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