A276164 a(n) is the maximum first-player score of a "Coins in a Row" game over all permutations of coins 1..n with both players using a minimax strategy.

1, 2, 4, 7, 10, 15, 17, 26, 27, 40, 38, 57, 52, 77, 67, 100

Offset: 1

Author

Peter Kagey, Aug 22 2016

Keywords

• more
• nonn

Comments

a(2*n) = A005449(n) via [1, n+1, 2, n+2, ..., n, 2*n]

Examples

			a(1)  = 1  via [1]
a(2)  = 2  via [1,2]
a(3)  = 4  via [1,2,3]
a(4)  = 7  via [1,3,2,4]
a(5)  = 10 via [1,2,4,3,5]
a(6)  = 15 via [1,4,2,5,3,6]
a(7)  = 17 via [1,2,3,4,6,5,7]
a(8)  = 26 via [1,5,2,6,3,7,4,8]
a(9)  = 27 via [1,2,3,4,6,5,8,7,9]
a(10) = 40 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 first player's resulting score would be 4 + 3 = 7.
		

References

• Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 1-2.

Crossrefs

Cf. A276163.

Formula

a(n) = (A000217(n) + A276163(n))/2

Extensions

a(11)-a(16) from Bert Dobbelaere, May 03 2025