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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 (list; graph; refs; listen; history; text; internal format)
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(n-1) - a(n-2), 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

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Last modified June 24 17:58 EDT 2019. Contains 324330 sequences. (Running on oeis4.)