A137508 -id:A137508 - cp's OEIS frontend

A137583 Number of elements in the n-th period of the Janet periodic table of elements.

2, 2, 8, 8, 18, 18, 32, 32

Offset: 1

Paul Curtz, Apr 26 2008

Essentially 2 followed by the first terms of A093907.

This puts Hydrogen and Helium in the first row, Lithium and Beryllium into the second, Boron to Magnesium into the third etc.

Mark R. Leach, The Internet Database of Periodic Tables, Chemogenesis web book.
Albert Tarantola, PSE of Elements (Janet form).
Mark J. Winter, Image of the Janet long format (or 32-column) periodic table, Web Elements Chemistry Nexus.

Cf. A093907, A137508, A138509, A137575.

Flatten@ Table[2 (n #)^2 & /@ {-1, 1}, {n, 4}] (* Michael De Vlieger, Jul 22 2016 *)

Edited by R. J. Mathar, Oct 02 2009

A168281 Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.

Original entry on oeis.org

2, 2, 2, 2, 8, 2, 2, 8, 8, 2, 2, 8, 18, 8, 2, 2, 8, 18, 18, 8, 2, 2, 8, 18, 32, 18, 8, 2, 2, 8, 18, 32, 32, 18, 8, 2, 2, 8, 18, 32, 50, 32, 18, 8, 2, 2, 8, 18, 32, 50, 50, 32, 18, 8, 2, 2, 8, 18, 32, 50, 72, 50, 32, 18, 8, 2, 2, 8, 18, 32, 50, 72, 72, 50, 32, 18, 8, 2, 2, 8, 18, 32, 50, 72, 98, 72

Offset: 1

Paul Curtz, Nov 22 2009

Row sums are A099956(n-1) = 2*A005993(n-1).
The flattened triangle is simply 2 followed by A137508.
If A106314 is interpreted as a triangle, T(n,m) = 2*A106314(n,m).

			The table starts in row n=1 with columns 1<=m<=n as:
  2;
  2,2;
  2,8,2;
  2,8,8,2;
  2,8,18,8,2;
  2,8,18,18,8,2;
  ...

Michael De Vlieger, Table of n, a(n) for n = 1..10011 (First 141 rows).

Cf. A005993, A099956, A137508, A106314.

A168281 := proc(n,m) 2*(min(n+1-m,m))^2 ; end proc:
seq(seq(A168281(n,m),m=1..n),n=1..20) ;

Table[Map[2 Min[n + # - 1, #]^2 &, Drop[#, -Boole@ EvenQ@ n] ~Join~ Reverse@ # &@ Range@ Floor[n/2]], {n, 2, 14}] // Flatten (* Michael De Vlieger, Jul 19 2016 *)

Rephrased all comments in terms of a triangle by R. J. Mathar, Nov 24 2010
More terms from Michael De Vlieger, Jul 19 2016
Definition corrected by Georg Fischer, Nov 11 2021

A138300 Differences of each column for atomic numbers of Mendeleyev-Seaborg 7*32 elements periodic table,first extension,A138096 table.86 terms.Horizontal lecture.

Original entry on oeis.org

2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32

Offset: 0

Paul Curtz, May 07 2008

			First column differences: 2, 8, 8, 18, 18, 32; second: 8, 8, 18, 18, 32.
Table: 1 2, 11 8's, 27 18's, 47 32's
2.............................................................................................8
8..8...........................................................................8..8..8..8..8..8
8..8..........................................................................18.18.18.18.18.18
18.18.18...........................................18.18.18.18.18.18.18.18.18.18.18.18.18.18.18
18.18.18...........................................32.32.32.32.32.32.32.32.32.32.32.32.32.32.32
32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32.32

Cf. A093907, A137508, A137575, A137583, A138102.

cp's OEIS Frontend

A137583 Number of elements in the n-th period of the Janet periodic table of elements.

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A168281 Triangle T(n,m) = 2*(min(n - m + 1, m))^2 read by rows.

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A138300 Differences of each column for atomic numbers of Mendeleyev-Seaborg 7*32 elements periodic table,first extension,A138096 table.86 terms.Horizontal lecture.

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