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

0,2

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.

Links

Table of n, a(n) for n=0..63.

Example

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.

Sequence in context: A367004 A328298 A002374 * A226482 A338777 A110560

Adjacent sequences: A261043 A261044 A261045 * A261047 A261048 A261049

Keyword

nonn,tabf

Author

Paul Curtz, Nov 19 2015

Status

approved