23 Jun
2015
23 Jun
'15
6:01 p.m.
Closed form (as square = triangular): ( (sqrt(2)+1)^(2*n)/(4*sqrt(2)) - (1-sqrt(2))^(2*n)/(4*sqrt(2)) )^2 = (1/2) * ( ( (sqrt(2)+1)^n / 2 - (sqrt(2)-1)^n / 2 )^2 + 1 )*( (sqrt(2)+1)^n / 2 - (sqrt(2)-1)^n / 2 )^2. - Bill Gosper <http://oeis.org/wiki/User:Bill_Gosper>, Jul 25 2008 And for the Mathematica section(?): ChebyshevU[-1 + n, 3]^2 == Binomial[ChebyshevT[n/2, 3]^2, 2]; % /. n -> Range@9 Out[20]= True