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A169686 a(n) = sqrt(T(k-1)*T(k)*T(k+1) as k runs through the terms of A072221 and T(i)=i*(i+1)/2. 0
0, 30, 5850, 1157730, 229221540, 45384688830, 8985939059790, 1779170548525890, 352266782665431240, 69747043797185672190, 13809562405059974172930, 2734223609158076980818690, 541362465050894178032921580, 107187033856467889149087366750, 21222491341115591157198758976630 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

It is known (see Beiler, p. 198) that the product of three consecutive triangular numbers, T(k-1)T(k)T(k+1), is a square if (and only if?) 2k+1 = 3a for a in A001541. The corresponding values of k are in A072221.

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, 1966.

LINKS

Table of n, a(n) for n=1..15.

FORMULA

Empirical g.f.: 30*x^2*(x^2-9*x+1) / ((x^2-198*x+1)*(x^2-6*x+1)). - Colin Barker, Jul 26 2013

EXAMPLE

sqrt (T(3)T(4)T(5)) = 30

sqrt (T(24)T(25)T(26)) = 5850

sqrt (T(147)T(148)T(149)) = 1157730

sqrt (T(864)T(865)T(866)) = 229221540

CROSSREFS

Sequence in context: A206647 A321427 A050984 * A184889 A300147 A087216

Adjacent sequences:  A169683 A169684 A169685 * A169687 A169688 A169689

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 13 2010, based on an email from Neven Juric, Mar 19 2010

STATUS

approved

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Last modified October 22 16:15 EDT 2021. Contains 348174 sequences. (Running on oeis4.)