%I #8 May 01 2021 09:29:01
%S 1,2,3,2,1,4,3,2,2,1,1,1,5,3,2,1,2,1,1,1,6,3,2,1,1,2,1,1,1,7,3,2,1,1,
%T 1,2,1,1
%N Each row is a finite sequence of N terms a0, a1, ..., ai, ..., an which satisfies the conditions written in the following array: "In this array, there are a0 times the number 0, there are a1 times the number 1, ..., there are ai times the number i, ..., there are an times the number n".
%C In the generating array as above, the total of the first column of numbers is 2+2*n, the total of the second column is n*(n+1)/2, the total of all the numbers is (n+1)*(n+4)/2 and is equal to the sum of all the products i*ai. These properties are useful to get a fast computation.
%F For n<6, there exists only one sequence of 4 terms (n=3) (1,2,3,2).
%F For n>=6 there is always a sequence with a0=1 a1=n-2 a2=3 a3=2 a(n-2)=2, and all others ai=1.
%e In this array there is once the number 0,
%e there are 2 times the number 1,
%e there are 3 times the number 2,
%e there are 2 times the number 3,
%e so the first row is 1,2,3,2.
%K fini,nonn,uned
%O 3,2
%A Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 08 2007