0,3

The (labeled) case for k<=2 is given by A000225. The unlabeled analogue for k<=2 is given by A028310 (A000027). The unlabeled analogue for k<=3 is given by A000124.

Alice and Bob went out for dinner; Alice paid 10 euro for the taxi, Bob paid 20 euro for the dinner; if they have to equally divide the expenses Alice will have to give 5 euro to Bob. With two people, Alice and Bob, there are three possible cases: Alice has to give money to Bob, Bob has to give money to Alice, they paid the same amount, so no debtors nor creditors. With three people, there are 13 cases, with four people there are 51 cases and so on. - Alessandro Gentilini (alessandro.gentilini(AT)gmail.com), Aug 10 2006

Thomas Wieder, Home Page.

Thomas Wieder, (Old) Home Page.

egf = 2*exp(z)-2*exp(z)^2+exp(z)^3; ogf = -(-1+3*z-6*z^2)/(11*z^2+1-6*z-6*z^3). a(n) = 3^n+2-2*2^n; recurrence: a(n+3)-6*a(n+2)+11*a(n+1)-6*a(n), a(0) = 1, a(1) = 1, a(2) = 3.

A101052 := n -> 3^n+2-2*2^n; [ seq(3^n+2-2*2^n, n=0..30) ];

Cf. A000670, A000225, A000124, A028310, A097237.

Sequence in context: A116427 A008827 A026529 this_sequence A016064 A163774 A014985

Adjacent sequences: A101049 A101050 A101051 this_sequence A101053 A101054 A101055

nonn

Thomas Wieder (wieder.thomas(AT)t-online.de), Nov 28 2004