A261046 Irregular triangle read by rows: the first column consists of the odd numbers repeated but without the first 1. Row n (n>=0) contains floor(n/2)=1 terms. Every row contains successive odd numbers.

1, 3, 3, 5, 5, 7, 5, 7, 9, 7, 9, 11, 7, 9, 11, 13, 9, 11, 13, 15, 9, 11, 13, 15, 17, 11, 13, 15, 17, 19, 11, 13, 15, 17, 19, 21, 13, 15, 17, 19, 21, 23, 13, 15, 17, 19, 21, 23, 25, 15, 17, 19, 21, 23, 25, 27, 13, 15, 17, 19, 21, 23, 25, 27

Offset: 0

Author

Paul Curtz, Nov 19 2015

Keywords

• nonn
• tabf

Comments

A131507(n), not in the same order.

a(n) multiplied by the triangle (extended A249947(n+1)) = (A167268(n+1))/2 is

1, 1, 1,

3, 1, 3,

3, 5, 3, 1, 9, 5,

5, 7, * 3, 1, = 15, 7,

5, 7, 9, 5, 3, 1, 25, 21, 9

7, 9, 11, 5, 3, 1, 35, 27, 11,

etc. etc. etc.

The latter triangle is the odd numbers of A094728(n+1) which is

1,

4, 3,

9, 8, 5,

16, 15, 12, 7,

25, 24, 21, 16, 9,

etc.

Without the first column, the triangle is A120070(n+2). This gives a link between the frequencies of the spectral lines of the H-atom and the Janet periodic table of the elements.

Examples

			Triangle begins:
1,
3,
3,  5,
5,  7,
5,  7,  9,
7,  9, 11,
7,  9, 11, 13,
9, 11, 13, 15,
9, 11, 13, 15, 17,
....
		

Crossrefs

Cf. A094728, A120070, A131507, A167268, A249947.