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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.
2
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.
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
KEYWORD
nonn,tabf
AUTHOR
Paul Curtz, Nov 19 2015
STATUS
approved