0,1

Singmaster's problem: "A salesman's office is located on a straight road. His n customers are all located along this road to the east of the office, with the office of customer k at distance k from the salesman's office. The salesman must make a driving trip whereby he leaves the office, visits each customer exactly once, then returns to the office.

"Because he makes a profit on his mileage allowance, the salesman wants to drive as far as possible during his trip. What is the maximum possible distance he can travel on such a trip and how many different such trips are there?

"Assume that if the travel plans call for the salesman to visit customer j immediately after he visits customer i, then he drives directly from i to j."

The solution to the first question is twice A002620(n-1); the solution to the second question is a(n).

Number of permutation of [n] with no pair of consecutive elements of the same parity. - Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 26 2007

David Singmaster, Problem 1654, Mathematics Magazine 75 (October 2002). Solution in Mathematics Magazine 76 (October 2003).

Sequence in context: A145859 A145863 A110775 this_sequence A138262 A127510 A158810

Adjacent sequences: A092183 A092184 A092185 this_sequence A092187 A092188 A092189

nonn

N. J. A. Sloane (njas(AT)research.att.com), based on correspondence from Hugo Pfoertner and Rob Pratt, Apr 02 2004