A276165 a(n) is the first-player score difference of a "Coins in a Row" game over the n-th row of A066099 using a minimax strategy.

0, 1, 2, 0, 3, 1, 1, 1, 4, 2, 0, 2, 2, 0, 2, 0, 5, 3, 1, 3, 1, 1, 1, 1, 3, -1, 1, 1, 3, 1, 1, 1, 6, 4, 2, 4, 0, 2, 2, 2, 2, 0, 2, 0, 2, 2, 0, 2, 4, -2, 0, 2, 2, 0, 2, 0, 4, 2, 0, 0, 2, 0, 2, 0, 7, 5, 3, 5, 1, 3, 3, 3, 1, 1, 3, 1, 1, 3, 1, 3, 3, -1, 1, 1, 3, 1

Offset

0,3

Comments

"Coins in a Row" is a game in which players alternate picking up coins of varying denominations from the end of the row in an attempt to collect as many points as possible.

When a(n) is negative, the second player has a strategy that is guaranteed to collect more points.

References

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

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

Formula

a(n) = A276166(n) - A276167(n).

Example

Let [R,L,L,L] represent a game in which the first player takes the right coin, the second player takes the left coin, the first player takes the left coin, and the second player takes the left (only remaining) coin.
A066099_Row(0)    = [0];         a(0)    = 0  via [L]
A066099_Row(1)    = [1];         a(1)    = 1  via [L]
A066099_Row(3)    = [1,1];       a(3)    = 0  via [R,L]
A066099_Row(22)   = [2,1,2];     a(22)   = 1  via [L,R,L]
A066099_Row(88)   = [2,1,4];     a(88)   = 3  via [R,L,L]
A066099_Row(1418) = [2,1,4,2,2]; a(1418) = -1 via [L,R,R,R,L]

Prog

(Haskell)
minimax [] = 0
minimax as = max (head as - minimax (tail as)) (last as - minimax (init as))
a276165 = minimax . a066099_row

Crossrefs

Cf. A276163, A276164, A276166, A276167.

Sequence in context: A113504 A358726 A357623 * A344618 A124754 A357624

Adjacent sequences: A276162 A276163 A276164 * A276166 A276167 A276168

Keyword

sign

Author

Peter Kagey, Aug 25 2016

Status

approved