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 A204767 Quadruples (a,b,c,d) of the form ( n*(n^3-1), n^3-1, 2*n^3+1, n*(n^3+2) ). 1
 0, 0, 3, 3, 14, 7, 17, 20, 78, 26, 55, 87, 252, 63, 129, 264, 620, 124, 251, 635, 1290, 215, 433, 1308, 2394, 342, 687, 2415, 4088, 511, 1025, 4112, 6552, 728, 1459, 6579, 9990, 999, 2001, 10020, 14630, 1330, 2663, 14663, 20724, 1727, 3457, 20760, 28548, 2196, 4395, 28587 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Four consecutive (a,b,c,d) in the sequence are solutions to a^3+b^3+c^3 = d^3, that is a(4k+1)^3+a(4k+2)^3+a(4k+3)^3 = a(4k+4)^3. Also, A058895(n)^3 + A068601(n)^3 + A033562(n)^3 = A185065(n)^3. The sequence corresponds to the case m=1 in the identity (n*(n^3-m^3))^3+(m*(n^3-m^3))^3+(m*(2*n^3+m^3))^3 = (n*(n^3+2*m^3))^3. G. H. Hardy and E. M. Wright gave this identity in their "An Introduction to the Theory of Numbers" together with (n*(n^3-2*m^3))^3+(m*(n^3+m^3))^3+(m*(2*n^3-m^3))^3 = (n*(n^3+m^3))^3 (see References). - Bruno Berselli, Mar 13 2012 REFERENCES G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford University Press, 2008 (Sixth edition), Par. 13.7. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 MATHEMATICA Flatten[Table[{n^4 - n, n^3 - 1, 2 n^3 + 1, n^4 + 2 n}, {n, 1, 40}]] (* Vincenzo Librandi, Jan 02 2014 *) PROG (MAGMA) &cat[[n*(n^3-1), n^3-1, 2*n^3+1, n*(n^3+2)]: n in [1..40]]; CROSSREFS Cf. A058895, A068601, A033562, A185065. Sequence in context: A288803 A288334 A186764 * A287904 A287946 A288652 Adjacent sequences:  A204764 A204765 A204766 * A204768 A204769 A204770 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Mar 04 2012 STATUS approved

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)