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

Offset

1,2

Comments

a(2*n) = A005449(n) 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.

Links

Table of n, a(n) for n=1..10.

Formula

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

Example

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.

Crossrefs

Cf. A276163.

Sequence in context: A056750 A171926 A171930 * A306221 A095116 A027384

Adjacent sequences: A276161 A276162 A276163 * A276165 A276166 A276167

Keyword

more,nonn

Author

Peter Kagey, Aug 22 2016

Status

approved