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 A003556 Numbers that are both square and tetrahedral. 3
 0, 1, 4, 19600 (list; graph; refs; listen; history; text; internal format)
 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 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] (* From Harvey P. Dale, Feb 01 2011 *) CROSSREFS Sequence in context: A258101 A265215 A070157 * A053015 A089210 A203037 Adjacent sequences:  A003553 A003554 A003555 * A003557 A003558 A003559 KEYWORD nonn,fini,full AUTHOR STATUS approved

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Last modified September 23 02:13 EDT 2018. Contains 315271 sequences. (Running on oeis4.)