This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A169686 #10 Dec 26 2023 12:19:31 %S A169686 0,30,5850,1157730,229221540,45384688830,8985939059790, %T A169686 1779170548525890,352266782665431240,69747043797185672190, %U A169686 13809562405059974172930,2734223609158076980818690,541362465050894178032921580,107187033856467889149087366750,21222491341115591157198758976630 %N 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. %C A169686 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. %D A169686 A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, 1966. %F A169686 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 %e A169686 sqrt (T(3)T(4)T(5)) = 30 %e A169686 sqrt (T(24)T(25)T(26)) = 5850 %e A169686 sqrt (T(147)T(148)T(149)) = 1157730 %e A169686 sqrt (T(864)T(865)T(866)) = 229221540 %K A169686 nonn %O A169686 1,2 %A A169686 _N. J. A. Sloane_, Apr 13 2010, based on an email from Neven Juric, Mar 19 2010