A240061 Triangle read by rows, n>=1, 1<=k<=n. T(n,k) = number of cells in k-th row = number of cells in the k-th column of the diagram of the symmetric representation of sigma(n) in the first quadrant.

1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 0, 3, 1, 1, 1, 3, 2, 4, 1, 1, 1, 1, 0, 0, 4, 1, 1, 1, 1, 3, 2, 1, 5, 1, 1, 1, 1, 1, 1, 2, 0, 5, 1, 1, 1, 1, 1, 3, 1, 2, 1, 6, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6, 1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7

Offset: 1

Author

Omar E. Pol, Apr 26 2014

Keywords

• nonn
• tabl

Comments

Since the diagram is symmetric the number of cells in the k-th row equals the number of cells in k-th column, see example.

Row sums give A000203.

Right border gives A008619, n >= 1.

If n is an odd prime then row n lists (n+1)/2 ones, ((n+1)/2 - 2) zeros, and (n+1)/2.

Examples

			Triangle begins:
1;
1, 2;
1, 1, 2;
1, 1, 2, 3;
1, 1, 1, 0, 3;
1, 1, 1, 3, 2, 4;
1, 1, 1, 1, 0, 0, 4;
1, 1, 1, 1, 3, 2, 1, 5;
1, 1, 1, 1, 1, 1, 2, 0, 5;
1, 1, 1, 1, 1, 3, 1, 2, 1, 6;
1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 6;
1, 1, 1, 1, 1, 1, 4, 3, 4, 3, 1, 7;
1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 7;
...
For n = 9 the symmetric representation of sigma(9) = 13 in the first quadrant looks like this:
y
.                               Number of cells
._ _ _ _ _
|_ _ _ _ _|                            5
.         |_ _                         0
.         |_  |                        2
.           |_|_ _                     1
.               | |                    1
.               | |                    1
.               | |                    1
.               | |                    1
. . . . . . . . |_| . . x              1
.
So the 9th row of triangle is [1, 1, 1, 1, 1, 1, 2, 0, 5].
For n = 9 and k = 7 there are two cells in the 7th row of the diagram, also there are two cells in the 7th column of the diagram, so T(9,7) = 2.
		

Links

• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240060.