

A276166


a(n) is the first player's score in a "Coins in a Row" game over the nth row of A066099 using a minimax strategy.


3



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


REFERENCES

Peter Winkler, Mathematical Puzzles: A Connoisseur's Collection, A K Peters/CRC Press, 2003, pages 12.


LINKS

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


FORMULA

a(n) = A029837(n + 1)  A276167(n).
a(n) = A276165(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) = 1 via [R,L]
A066099_Row(22) = [2,1,2]; a(22) = 3 via [L,R,L]
A066099_Row(88) = [2,1,4]; a(88) = 5 via [R,L,L]
A066099_Row(1418) = [2,1,4,2,2]; a(1418) = 5 via [L,R,R,R,L]


PROG

(Haskell)
minimaxDifference [] = 0
minimaxDifference as = max (head as  minimaxDifference (tail as)) (last as  minimaxDifference (init as))
minimaxScore as = (sum as + minimaxDifference as) `div` 2
a276166 = minimaxScore . a066099_row


CROSSREFS

Cf. A276163, A276164, A276165, A276167.
Sequence in context: A297167 A325224 A303389 * A177062 A133924 A023135
Adjacent sequences: A276163 A276164 A276165 * A276167 A276168 A276169


KEYWORD

nonn


AUTHOR

Peter Kagey, Aug 25 2016


STATUS

approved



