A240060 Triangle read by rows, n>=1, 1<=k<=n. T(n,n-k+1) = number of cells in the 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, 2, 1, 2, 1, 1, 3, 2, 1, 1, 3, 0, 1, 1, 1, 4, 2, 3, 1, 1, 1, 4, 0, 0, 1, 1, 1, 1, 5, 1, 2, 3, 1, 1, 1, 1, 5, 0, 2, 1, 1, 1, 1, 1, 1, 6, 1, 2, 1, 3, 1, 1, 1, 1, 1, 6, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 7, 1, 3, 4, 3, 4, 1, 1, 1, 1, 1, 1, 7, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1

Offset

1,2

Comments

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

Row sums give A000203.

Column 1 gives A008619, n >= 1.

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

Mirror of A240061.

Links

Table of n, a(n) for n=1..91.

Index entries for sequences related to sigma(n)

Example

Triangle begins:
1;
2, 1;
2, 1, 1;
3, 2, 1, 1;
3, 0, 1, 1, 1;
4, 2, 3, 1, 1, 1;
4, 0, 0, 1, 1, 1, 1;
5, 1, 2, 3, 1, 1, 1, 1;
5, 0, 2, 1, 1, 1, 1, 1, 1;
6, 1, 2, 1, 3, 1, 1, 1, 1, 1;
6, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1;
7, 1, 3, 4, 3, 4, 1, 1, 1, 1, 1, 1;
7, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1;
...
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 [5, 0, 2, 1, 1, 1, 1, 1, 1].
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(9,9-7+1) = T(9,3) = 2.

Crossrefs

Cf. A000203, A008619, A024916, A196020, A236104, A235791, A237270, A237271, A237591, A237593, A239660, A239931-A239934, A240061.

Sequence in context: A347045 A323345 A135539 * A129264 A135840 A228570

Adjacent sequences: A240057 A240058 A240059 * A240061 A240062 A240063

Keyword

nonn,tabl

Author

Omar E. Pol, Apr 26 2014

Status

approved