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.
a[ n_ ] := Module[ {}, If[ n==2, Return[ 1 ] ]; For[ f0=3; f1=2; f2=1; c=0, f0<=n, f0=(f2=f1)+(f1=f0), If[ Mod[ n-f0, f2 ]==0, c++ ] ]; c ]; For[ n=1; max=-1, True, n++, If[ a[ n ]>max, Print[ n ]; max=a[ n ] ] ]
For n=2, the single solution is the third term of the Fibonacci sequence (k=1), so a(2)=1. For n=3, we observe the value as the fourth term for k=1, and the third term for k=2 for a total count of a(3) = 2. For n=4, we have k=2 and k=3, so a(4) = 2. For n=5, we have k=1, k=3, k=4.
a(n) = my(c, x, y=1); while(n>=x+=2*y, y=x-y; x-=y; if((n-y)%x==0, c++)); c; \\ Jinyuan Wang, Mar 20 2021
def get_val(n):
res = 0
for k in range(1, n):
(a, b) = (k, 1)
while b < n:
(a, b) = (b, a+b)
if b == n:
res += 1
return res
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