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A286930 Integers whose double is a square and whose triple is a cube.

%I A286930 #25 Oct 19 2024 15:57:32
%S A286930 0,72,4608,52488,294912,1125000,3359232,8470728,18874368,38263752,
%T A286930 72000000,127552392,214990848,347530248,542126592,820125000,
%U A286930 1207959552,1737904968,2448880128,3387303432,4608000000,6175160712,8163353088,10658584008,13759414272,17578125000
%N A286930 Integers whose double is a square and whose triple is a cube.
%H A286930 Colin Barker, <a href="/A286930/b286930.txt">Table of n, a(n) for n = 1..1000</a>
%H A286930 Ana Rechtman, <a href="http://images-archive.math.cnrs.fr/Mai-2017-2e-defi.html">Mai 2017, 2e défi</a>, Images des Mathématiques, CNRS, 2017 (in French).
%H A286930 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A286930 a(n) = 72*(n-1)^6. - _David A. Corneth_, May 16 2017
%F A286930 O.g.f.: 72*x^2*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7. - _Colin Barker_, May 17 2017
%F A286930 E.g.f.: 72*(-1 + (1 - x + x^2 + 10*x^3 + 20*x^4 + 9*x^5 + x^6)*exp(x)). - _Bruno Berselli_, May 17 2017
%e A286930 From _Michael De Vlieger_, May 16 2017: (Start)
%e A286930 72 is a term because 2*72 = 144 = 12^2 and 3*72 = 216 = 6^3.4608 is a term because 2*4608 = 96^2 and 3*4608 = 24^3. (End)
%t A286930 Array[72 (# - 1)^6 &, 26] (* _Michael De Vlieger_, May 16 2017 *)
%t A286930 LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,72,4608,52488,294912,1125000,3359232},30] (* _Harvey P. Dale_, May 07 2022 *)
%o A286930 (PARI) isok(x) = issquare(2*x) && ispower(3*x, 3);
%o A286930 (PARI) concat(0, Vec(72*x^2*(1 + x)*(1 + 56*x + 246*x^2 + 56*x^3 + x^4) / (1 - x)^7 + O(x^30))) \\ _Colin Barker_, May 17 2017
%Y A286930 Cf. A001014.
%Y A286930 Intersection of A001105 and A244728.
%K A286930 nonn,easy
%O A286930 1,2
%A A286930 _Michel Marcus_, May 16 2017
%E A286930 More terms from _Michael De Vlieger_, May 16 2017