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A241924 16*s^8 - 168*s^4*t^4 + 9*t^8, where s > 0, t = 1..s. 3

%I

%S -143,1417,-36608,91377,-110448,-938223,1005577,362752,-2376023,

%T -9371648,6145009,4572304,-2195951,-20040176,-55859375,26656137,

%U 23392512,9296937,-28274688,-105690519,-240185088,91833457,85785232,59623057,-10435568,-156352559

%N 16*s^8 - 168*s^4*t^4 + 9*t^8, where s > 0, t = 1..s.

%C 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).

%C 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).

%H Vincenzo Librandi, <a href="/A241924/b241924.txt">Table of n, a(n) for n = 1..1000</a>

%H D. Alpern, <a href="http://www.alpertron.com.ar/SPOW432.HTM">List of first 1602 solutions to a^4 + b^3 = c^2 for increasing values of a, where gcd(a,b,c) = 1</a>.

%H D. Alpern, Sum of powers, <a href="http://www.alpertron.com.ar/SUMPOWER.HTM#P4_3_2">a^4 + b^3 = c^2</a>.

%H H. Cohen, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=557612&amp;messageID=1674064#1674064">a^m + b^n = c^p (was: Sum of two powers = Square)</a>, Sci.Math.Research posting to Jan 09 1998.

%t Flatten[Table[16 s^8 - 168 s^4 t^4 + 9 t^8, {s, 10}, {t, s}]]

%o (MAGMA) [16*s^8-168*s^4*t^4+9*t^8: t in [1..s], s in [1..10]];

%Y Cf. A096741, A241923, A241925.

%K sign

%O 1,1

%A _Vincenzo Librandi_, May 02 2014

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Last modified March 20 05:17 EDT 2019. Contains 321344 sequences. (Running on oeis4.)