A378734 - OEIS

%I #14 Dec 12 2024 09:30:11

%S 1,2,6,23,108,579,3447,22190,152407,1103566,8355894,65701413

%N Number of multisets E(n) generable by the following procedure: E(0) = { 0, 0, ... }; to get an E(n+1) from an E(n), first increment all elements then optionally choose  an x and a y and replace them with 0 and x+y.

%C Let there be an infinite number of producers whose initial stocks are equal to 0. At each step (n >= 1), each producer produces 1 resource and adds it to its stock; then a facetious imp may decide to move one producer's stock to another's. a(n) is the number of possible configurations after n steps.

%e E(0) is:

%e         { 0, 0, 0, 0, 0, 0, ... }

%e E(1) can be:

%e    A := { 1, 1, 1, 1, 1, 1, ... } // A = E(0) + 1

%e    B := { 0, 2, 1, 1, 1, 1, ... } // B is A where a 1 moved onto a 1: B = A<1,1>

%e E(2) can be:

%e    C := { 2, 2, 2, 2, 2, 2, ... } // C = A + 1

%e    D := { 1, 3, 2, 2, 2, 2, ... } // D = B + 1

%e         { 0, 4, 2, 2, 2, 2, ... } // = C<2,2> = D<1,3> = D<3,1>

%e         { 0, 3, 3, 2, 2, 2, ... } // = D<1,2> = D<2,1>

%e         { 0, 1, 5, 2, 2, 2, ... } // = D<2,3> = D<3,2>

%e         { 0, 1, 3, 4, 2, 2, ... } // = D<2,2>

%e So, the sequence starts: 1, 2, 6, ...

%K nonn,more,new

%O 0,2

%A _Luc Rousseau_, Dec 06 2024