A004278 1, 3 and the positive even numbers.

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

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 * A333183 A068670 A371925

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