A378734 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.

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

Offset: 0

Author

Luc Rousseau, Dec 06 2024

Keywords

• nonn
• more

Comments

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.

Examples

			E(0) is:
        { 0, 0, 0, 0, 0, 0, ... }
E(1) can be:
   A := { 1, 1, 1, 1, 1, 1, ... } // A = E(0) + 1
   B := { 0, 2, 1, 1, 1, 1, ... } // B is A where a 1 moved onto a 1: B = A<1,1>
E(2) can be:
   C := { 2, 2, 2, 2, 2, 2, ... } // C = A + 1
   D := { 1, 3, 2, 2, 2, 2, ... } // D = B + 1
        { 0, 4, 2, 2, 2, 2, ... } // = C<2,2> = D<1,3> = D<3,1>
        { 0, 3, 3, 2, 2, 2, ... } // = D<1,2> = D<2,1>
        { 0, 1, 5, 2, 2, 2, ... } // = D<2,3> = D<3,2>
        { 0, 1, 3, 4, 2, 2, ... } // = D<2,2>
So, the sequence starts: 1, 2, 6, ...