A003556 Numbers that are both square and tetrahedral.

0, 1, 4, 19600

Offset

1,3

Comments

A. J. J. Meyl proved in 1878 that only 1, 4 and 19600 are both square and tetrahedral. See link. [Bernard Schott, Dec 23 2012]

References

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 600.

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 165 (Rev. ed. 1997).

Links

Table of n, a(n) for n=1..4.

M. Gardner, Letter to N. J. A. Sloane, circa Aug 11 1980, concerning A001110, A027568, A039596, etc.

A. J. J. Meyl, Question 1194, Nouvelles Annales de Mathématiques, 2ème série, tome 17 (1878), p. 464-467.

Example

From Bernard Schott, Dec 23 2012: (Start)
If S(n) = n^2 and T(m) = m*(m+1)*(m+2)/6, then
-> S(1)= T(1) = 1;
-> S(2)= T(2) = 4;
-> S(140) = T(48) = 19600. (End)

Mathematica

Select[Rest[FoldList[Plus, 0, Rest[FoldList[Plus, 0, Range[50000]]]]], IntegerQ[Sqrt[ # ]]&]
Intersection[Binomial[# + 2, 3]&/@Range[0, 10000], Range[0, 409000]^2] (* Harvey P. Dale, Feb 01 2011 *)

Crossrefs

Intersection of A000290 and A000292.

Sequence in context: A258101 A265215 A070157 * A331667 A053015 A089210

Adjacent sequences: A003553 A003554 A003555 * A003557 A003558 A003559

Keyword

nonn,fini,full

Author

N. J. A. Sloane

Status

approved