

A269837


Irregular triangle read by rows: even terms of A094728(n+1) divided by 4.


2



1, 2, 4, 3, 6, 4, 9, 8, 5, 12, 10, 6, 16, 15, 12, 7, 20, 18, 14, 8, 25, 24, 21, 16, 9, 30, 28, 24, 18, 10, 36, 35, 32, 27, 20, 11, 42, 40, 36, 30, 22, 12, 49, 48, 45, 40, 33, 24, 13, 56, 54, 50, 44, 36, 26, 14, 64, 63, 60, 55, 48, 39, 28, 15
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OFFSET

0,2


COMMENTS

See A264798 and A261046 for the Hydrogen atom and the Janet periodic table.
Decomposition by multiplication i.e. a(n) = b(n)*c(n) by irregular triangle:
1, 1 1,
2, 1 2,
4, 3, 2, 1, 2, 3,
6, 4, = 2, 1, * 3, 4,
9, 8, 5, 3, 2, 1, 3, 4, 5,
12, 10, 6, 3, 2, 1, 4, 5, 6,
16, 15, 12, 7, 4, 3, 2, 1, 4, 5, 6, 7,
etc. etc. etc.
Decomposition by subtraction, a(n) = d(n)  e(n):
1, 1 0,
2, 2, 0,
4, 3, 4, 3, 0, 0,
6, 4, = 6, 5,  0, 1,
9, 8, 5, 9, 8, 7, 0, 0, 2,
12, 10, 6, 12, 11, 10, 0, 1, 4,
16, 15, 12, 7, 16, 15, 14, 13, 0, 0, 2, 6,
20, 18, 14, 8, 20, 19, 18, 17, 0, 1, 4, 9,
etc. etc. etc.
d(n) is the natural numbers A000027 inverted by lines. e(n) will be studied (see A239873).
Sum of a(n) by diagonals: 1, 5, 13, 27, 48, ... . The third differences have the period 2: repeat 2, 1. See A002717.


LINKS



MATHEMATICA

Table[(n + 1)^2  k^2, {n, 15}, {k, 0, n  1}]/4 /. _Rational > Nothing // Flatten (* Michael De Vlieger, Mar 07 2016 *)


CROSSREFS

Cf. A000027, A000034, A002717, A004736, A094728, A122197, A138099, A167430, A239873, A261046, A264798.


KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



