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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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See A264798 and A261046 for the Hydrogen atom and the Janet periodic table.
a(n) odd terms are again A264798.
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.
b(n) is duplicated A004736(n) or mirror of A122197(n+1). c(n) = A138099(n+1).
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
Sequence in context: A057956 A151734 A175027 * A308982 A182298 A182732
KEYWORD
nonn,tabf
AUTHOR
Paul Curtz, Mar 06 2016
STATUS
approved

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Last modified July 18 07:53 EDT 2024. Contains 374377 sequences. (Running on oeis4.)