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S. Barbero, U. Cerruti, and N. Murru, <a href="http://www.seminariomatematico.polito.it/rendiconti/78-1/BarberoCerrutiMurru.pdf">On polynomial solutions of the Diophantine equation (x + y - 1)^2 = wxy</a>, Rendiconti Sem. Mat. Univ. Pol. Torino (2020) Vol. 78, No. 1, 5-12.
LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 20] &[16] (* Michael De Vlieger, Feb 23 2021 *)
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Also n m such that (3*nm^2 + nm)/4 = nm*(3*n m + 1)/4 is a perfect square. - Ctibor O. Zizka, Oct 15 2010
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a(n) = (A001075(n)^2-1)/3 . - Parker Grootenhuis, Nov 28 2017
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