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A286930
Integers whose double is a square and whose triple is a cube.
2
0, 72, 4608, 52488, 294912, 1125000, 3359232, 8470728, 18874368, 38263752, 72000000, 127552392, 214990848, 347530248, 542126592, 820125000, 1207959552, 1737904968, 2448880128, 3387303432, 4608000000, 6175160712, 8163353088, 10658584008, 13759414272, 17578125000
OFFSET
1,2
LINKS
Ana Rechtman, Mai 2017, 2e défi, Images des Mathématiques, CNRS, 2017 (in French).
FORMULA
a(n) = 72*(n-1)^6. - David A. Corneth, May 16 2017
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
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
EXAMPLE
From Michael De Vlieger, May 16 2017: (Start)
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)
MATHEMATICA
Array[72 (# - 1)^6 &, 26] (* Michael De Vlieger, May 16 2017 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 72, 4608, 52488, 294912, 1125000, 3359232}, 30] (* Harvey P. Dale, May 07 2022 *)
PROG
(PARI) isok(x) = issquare(2*x) && ispower(3*x, 3);
(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
CROSSREFS
Cf. A001014.
Intersection of A001105 and A244728.
Sequence in context: A060507 A238772 A225831 * A327375 A054557 A167871
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, May 16 2017
EXTENSIONS
More terms from Michael De Vlieger, May 16 2017
STATUS
approved