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A152005
Numbers whose square is the product of two distinct tetrahedral numbers A000292.
1
2, 140, 280, 1092, 166460, 189070, 665840, 804540, 845460, 34250920, 38336088, 133784560, 138535992, 225792840, 4998790160, 6301258040, 7559616818, 8367691640, 39991371446, 104637102152, 227490888350, 1497809326860, 296523233581822
OFFSET
1,1
COMMENTS
There may be values that are not given in the recurrence shown. This sequence is suggested by Ulas, p. 11, who supplied the recurrence.
a(24) > 3*10^14. - Donovan Johnson, Jan 11 2012
FORMULA
a(n) = T(i)*T(j) where T(k) = A000292(k) = C(k+2,3) = k*(k+1)*(k+2)/6.
EXAMPLE
From R. J. Mathar, Jan 22 2009: (Start)
2 is in the sequence because 2^2 = 4*1 = T(2)*T(1).
140 is in the sequence 140^2 = 560*35 = T(14)*T(5) = 19600*1 = T(48)*T(1).
280 is in the sequence because 280^2 = 19600*4 = T(48)*T(2).
1092 is in the sequence because 1092^2 = 3276*364 = T(26)*T(12). (End)
MATHEMATICA
(* This program is not suitable to compute more than a dozen terms. *)
terms = 12; imin = 1; imax = 3000;
Union[Reap[Do[k2 = i(i+1)(i+2)/6 j(j+1)(j+2)/6; k = Sqrt[k2]; If[IntegerQ[k], Print[k]; Sow[k]], {i, imin, imax}, {j, i+1, imax}]][[2, 1]]][[1 ;; terms]] (* Jean-François Alcover, Oct 31 2018 *)
CROSSREFS
Cf. A000292, A175497 (products distinct triangular numbers).
Sequence in context: A265176 A101232 A093887 * A140898 A220513 A120814
KEYWORD
nonn,more
AUTHOR
Jonathan Vos Post, Nov 19 2008
EXTENSIONS
Sequence replaced by sequence with no intermediate terms missing by R. J. Mathar, Jan 22 2009
a(15)-a(18) from Donovan Johnson, Jan 24 2009
a(19)-a(23) from Donovan Johnson, Jan 11 2012
STATUS
approved