cp's OEIS Frontend

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.

%I A378734 #14 Dec 12 2024 09:30:11
%S A378734 1,2,6,23,108,579,3447,22190,152407,1103566,8355894,65701413
%N 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.
%C A378734 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 A378734 E(0) is:
%e A378734         { 0, 0, 0, 0, 0, 0, ... }
%e A378734 E(1) can be:
%e A378734    A := { 1, 1, 1, 1, 1, 1, ... } // A = E(0) + 1
%e A378734    B := { 0, 2, 1, 1, 1, 1, ... } // B is A where a 1 moved onto a 1: B = A<1,1>
%e A378734 E(2) can be:
%e A378734    C := { 2, 2, 2, 2, 2, 2, ... } // C = A + 1
%e A378734    D := { 1, 3, 2, 2, 2, 2, ... } // D = B + 1
%e A378734         { 0, 4, 2, 2, 2, 2, ... } // = C<2,2> = D<1,3> = D<3,1>
%e A378734         { 0, 3, 3, 2, 2, 2, ... } // = D<1,2> = D<2,1>
%e A378734         { 0, 1, 5, 2, 2, 2, ... } // = D<2,3> = D<3,2>
%e A378734         { 0, 1, 3, 4, 2, 2, ... } // = D<2,2>
%e A378734 So, the sequence starts: 1, 2, 6, ...
%K A378734 nonn,more
%O A378734 0,2
%A A378734 _Luc Rousseau_, Dec 06 2024