A129773 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".

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, 1, 2, 1, 1

Offset

3,2

Comments

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.

Links

Table of n, a(n) for n=3..40.

Formula

For n<6, there exists only one sequence of 4 terms (n=3) (1,2,3,2).

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.

Example

In this array there is once the number 0,
there are 2 times the number 1,
there are 3 times the number 2,
there are 2 times the number 3,
so the first row is 1,2,3,2.

Crossrefs

Sequence in context: A118457 A319247 A343180 * A105789 A259579 A076549

Adjacent sequences: A129770 A129771 A129772 * A129774 A129775 A129776

Keyword

fini,nonn,uned

Author

Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 08 2007

Status

approved