

A004278


1, 3 and the positive even numbers.


3



1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104
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OFFSET

1,2


COMMENTS

a(n) is the maximum number of turns that player A needs to identify with certainty the location of the coin that player B has hidden in one box in a row of n + 1 boxes. Player A starts by opening one of the boxes to see if the coin is in that box. After that, B secretly relocates the coin from its current box to one of the neighboring boxes, except when n = 1. In that case the game ends before B can relocate the coin. On each turn player A opens one box and when player A can tell in which box the coin is located, the game ends. Can be proved.  Bob Andriesse, Dec 22 2017


LINKS

Iain Fox, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (2,1)


FORMULA

From Iain Fox, Dec 21 2017: (Start)
G.f.: (x + x^5)/(1  x)^2.
a(n) = 2*a(n1)  a(n2), n > 2 and n is not 5.
a(n) = 2*n  2 + floor((4/Pi)*arctan(2  n)).
(End)
E.g.f.: 2*e^x*(x  1) + 3 + 2*x + x^2/2.  Iain Fox, Dec 22 2017
a(n) = (abs(4  n) + 3*n  4)/2.  Iain Fox, Dec 23 2017


MATHEMATICA

Sort[Join[{1, 3}, 2*Range[60]]] (* Harvey P. Dale, Feb 04 2015 *)


PROG

(Haskell)
a004278 n = if n <= 3 then n else 2 * (n  2)
a004278_list = [1, 2, 3] ++ [4, 6 ..]
 Reinhard Zumkeller, Nov 10 2012
(PARI) first(n) = Vec((x + x^5)/(x  1)^2 + O(x^(n+1))) \\ Iain Fox, Dec 21 2017


CROSSREFS

Cf. A005843.
Sequence in context: A032954 A158023 A004271 * A068670 A084925 A045718
Adjacent sequences: A004275 A004276 A004277 * A004279 A004280 A004281


KEYWORD

easy,nonn


AUTHOR

N. J. A. Sloane


EXTENSIONS

Offset corrected by Reinhard Zumkeller, Nov 10 2012


STATUS

approved



