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There are very many possible solutions. The simplest polynomial solution is t(n) = (n^4 - 14n^3 + 71n^2 + 14n + 24)/24.
t(3) = 10 - 32 = 1
tn=5n-3
It is: 25-7n
-4n + 24 #1 ; -4(1) +24 = 20 #2 ; -4(2) + 24 = 16 #3 ; =4(3) + 24 = 12