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A078476 Time taken to get n people from one side of a bridge to the other where (a) the only flashlight must be carried when crossing; (b) only one or two people may cross at the same time; (c) a pair crosses at the speed of the slowest member; and (d) the k-th person's speed requires k seconds to cross the bridge. 1
1, 2, 6, 11, 16, 22, 28, 35, 42, 50, 58, 67, 76, 86, 96, 107, 118, 130, 142, 155, 168, 182, 196, 211, 226, 242, 258, 275, 292, 310, 328, 347, 366, 386, 406, 427, 448, 470, 492, 515, 538, 562, 586, 611, 636, 662, 688, 715, 742, 770, 798, 827, 856, 886, 916, 947 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Quasipolynomial of order 2. - Charles R Greathouse IV, Mar 26 2013
LINKS
Torsten Sillke, Crossing the bridge.
FORMULA
For n>1: a(n)=n^2/4+3n-5+((-1)^n-1)/8.
G.f.: x*(1+2*x^2+x^3-3*x^4)/((1-x)^3*(1+x)). [Colin Barker, Jun 07 2012]
Contribution from Denis Borris, Mar 26 2013: (Start)
n is even: a(n) = (n^2 + 12n - 20) / 4.
n is odd : a(n) = (n^2 + 12n - 21) / 4.
(End)
EXAMPLE
a(5)=16 since one of the fastest ways is for 1&2 to cross (time 2), 1 to return (1), 4&5 to cross (5), 2 to return (2), 1&3 to cross (3), 1 to return (1) and 1&2 to cross (2) for a total time of 2+1+5+2+3+1+2=16.
PROG
(PARI) a(n)=n^2\4+3*n-5 \\ Charles R Greathouse IV, Mar 26 2013
CROSSREFS
Sequence in context: A020966 A193910 A215918 * A217687 A212459 A099056
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jan 03 2003
STATUS
approved

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Last modified February 21 12:33 EST 2024. Contains 370235 sequences. (Running on oeis4.)