OFFSET
1,3
COMMENTS
a(2*n) = n^2 via [1, n+1, 2, n+2, ..., n, 2*n]
REFERENCES
Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.
EXAMPLE
a(1) = 1 via [1]
a(2) = 1 via [1,2]
a(3) = 2 via [1,2,3]
a(4) = 4 via [1,3,2,4]
a(5) = 5 via [1,2,4,3,5]
a(6) = 9 via [1,4,2,5,3,6]
a(7) = 6 via [1,2,3,4,6,5,7]
a(8) = 16 via [1,5,2,6,3,7,4,8]
a(9) = 9 via [1,2,3,4,6,5,8,7,9]
a(10) = 25 via [1,6,2,7,3,8,4,9,5,10]
For n=4, the first player would take 4, the second player would take 2, the first player would take 3, and the second player would take 1. The resulting score difference would be 4 - 2 + 3 - 1 = 4.
PROG
(Haskell)
minimax [] = 0
minimax as = max (head as - minimax (tail as)) (last as - minimax (init as))
a276163 n = maximum $ map minimax $ permutations [1..n]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Peter Kagey, Aug 22 2016
STATUS
approved