In mathematics, the Fibonacci numbers, commonly denoted as fnf_nfn, is a sequence such that each number is the sum of the two preceding numbers, starting with 1{1}1 and 1{1}1. That is, f1=1,f2=1f_1 = 1, f_2 = 1f1=1,f2=1 and fn=fn2+fn1(n≥3)f_n = f_{n-2} + f_{n-1}~fn=fn2+fn1(n≥3). Thus, the beginning of the sequence is 1,1,2,3,5,8,13,21,…. Given n{n}n, please calculate ∑i=1n∑j=i+1ngsum_{i=1}^{n}{sum_{j=i+1}^{n}{g}}∑i=1n∑j=i+1ng, where g(x,y)=1{g(x,y) = 1}g(x,y)=1 when xyx cdot yxy is even, otherwise g(x,y)=0{g(x,y) = 0}g(x,y)=0.
In mathematics, the Fibonacci numbers, commonly denoted as fnf_nfn, is a sequence such that each number is the sum of the two preceding numbers, starting with 1{1}1 and 1{1}1. That is, f1=1,f2=1f_1 = 1, f_2 = 1f1=1,f2=1 and fn=fn−2+fn−1 (n≥3)f_n = f_{n-2} + f_{n-1}~(n ge 3)fn=fn−2+fn−1 (n≥3). Thus, the beginning of the sequence is 1,1,2,3,5,8,13,21,…1, 1, 2, 3, 5, 8, 13, 21,ldots1,1,2,3,5,8,13,21,… . Given n{n}n, please calculate ∑i=1n∑j=i+1ng(fi,fj)sum_{i=1}^{n}{sum_{j=i+1}^{n}{g(f_i,f_j)}}∑i=1n∑j=i+1ng(fi,fj), where g(x,y)=1{g(x,y) = 1}g(x,y)=1 when x⋅yx cdot yx⋅y is even, otherwise g(x,y)=0{g(x,y) = 0}g(x,y)=0.
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