Number Sequence Game
Problem 477
The number sequence game starts with a sequence S of N numbers written on a line.
Two players alternate turns. At his turn, a player must select and remove either the first or the last number remaining in the sequence.
The player score is the sum of all the numbers he has taken. Each player attempts to maximize his own sum.
Player 1 score is 1 + 10 = 11.
Let F(N) be the score of player 1 if both players follow the optimal strategy for the sequence S = {s1, s2, ..., sN} defined as:
The sequence begins with S = {0, 45, 2070, 4284945, 753524550, 478107844, 894218625, ...}.
You are given F(2) = 45, F(4) = 4284990, F(100) = 26365463243, F(104) = 2495838522951.
Find F(108).