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The s-block is placed at

* the left, except row 1 (for Mendeleev-Moseley-Seaborg periodic table)

* the right (for Janet periodic table)

The number of elements in each block of Janet's periodic table are

s-block (1s to 8s): 8*2 = 16 elements;

p-block (2p to 7p): 6*6 = 36 elements;

d-block (3d to 6d): 4*10 = 40 elements;

f-block (4f to 5f): 2*14 = 28 elements.

The atomic numbers of elements in each block of Janet's periodic table are

s-block: 1,2, 3,4, 11,12, 19,20, 37,38, 55,56, 87,88, 119,120 (cf. A160914)

p-block: 5..10, 13..18, 31..36, 49..54, 81..86, 113..118 (cf. A138469)

d-block: 21..30, 39..48, 71..80, 103..112 (cf. A199934)

f-block: 57..70, 89..102 (cf. A217923).

The number of elements for each successive filled subshell are

s-block (1s): a(0)=2 terms (for H and He, i.e., 1 and 2);

s-block (2s): a(1)=2 terms (for Li and Be, i.e., 3 and 4);

p-block (2p): a(2)=6 terms (for B,C,N,O,F,Ne, i.e., 5 to 10);

s-block (3s): a(3)=2 terms (for Na,Mg, i.e., 11 and 12);

p-block (3p): a(4)=6 terms (for Al,Si,P,S,Cl,Ar, i.e., 13 to 18);

...

Reference, 2 leaflet 2, with Janet form (5). Extended.

From Daniel Forgues, May 09 2011: (Start)

Janet also envisaged an 'element zero' ('neutronium'?) - whose 'atom' would consist of two neutrons (and thus zero electrons, which would give a(0) = 0) and he speculated that this would be the link to a mirror-image table of elements with negative atomic numbers - in effect anti-matter (which would give a(-n) = -a(n), since positrons are negated electrons).

Maximum number of electrons for successive subshells of each shell of an atom, in the building up order (per aufbau principle and Madelung's rule).

Every term is twice an odd number since each filled subshell in block l has m going from -l to + l (2l+1 values,) each with 2 electrons (spin +1/2 and spin -1/2).

Blocks:

l=0: s (2 electrons) (first subshell of a shell, new period of Mendeleev's table)

l=1: p (6 electrons) (except for first shell, last subshell of a shell)

l=2: d (10 electrons)

l=3: f (14 electrons)

l=4: g (18 electrons)

...

l=l: ... (2*(2l+1) electrons)

The first subshell of the k-th shell has l = 0, k >= 1.

The second subshell of the k-th shell has l = floor(k/2), k >= 2.

The following subshells of the k-th shell have l decrementing down to 1, k >= 2.

(End)

Concatenation of finite arithmetic sequences, each followed by 2: { }, 2, { }, 2, {6}, 2, {6}, 2, {10, 6}, 2, {10, 6}, 2, {14, 10, 6}, 2, {14, 10, 6}, 2, {18, 14, 10, 6}, 2, {18, 14, 10, 6}, 2, ... - Daniel Forgues, May 15 2011

Named after the French mathematician Charles Janet (1849-1932). - Amiram Eldar, Jun 22 2021

See A168342. Must be included in A167268. From right to left, first vertical is A168380 from 1 to 8. Second vertical is A168380-1. In (1) page 12, introducing elements 93 to 120, Janet says that there is a probable 8th row. For row 8, he proposes, like for row 7, 32 elements (89 to 120). Page 16 he presents 4 blocks: first has 2*8 elements, second: 6*6, third: 10*4, fourth: 14*2. Today, blocks are s,p,d,f for Mendeleyev-Moseley-Seaborg 118 elements periodic table. See (2), (3), A173592 and A138509. In 1927, only 88 on the first 92 elements were known; 41 (1937 discovered), 61 (1947), 85 (1940) and 87 (1939) were missing. Since 2010 (117 discovered) the first 118 elements are known. Janet predicted only 120 elements.

After the s-block (A160914) and the p-block (A138469), we present the d-block (4*10) elements for the Janet table, in A167268. Janet published his table in a 1928 book (see below), 24 of planche 7, in which he also introduced the s, p, d, f blocks (called nappes 1, 2, 3, 4).

a(n) also comes from one of the two classical Mendeleyev-Moseley-Seaborg periodic table(s) i.e. (see A138096):

1 2

3 4 5 to 10

11 12 13 to 18

19 20 21 to 30 31 to 36

37 38 39 to 48 49 to 54

55 56 57 to 70 71 to 80 81 to 86

87 88 89 to 102 103 to 112 113 to 118.

(The second is in A134982).

From Paul Curtz, Oct 26 2012: (Start)

Tarantola's formulas for the Janet table:

Let D(n) = n*(n+1)*(n+2)/6 + (1-(-1)^n)*(n+1)/4 = A168380(n).

The row R at which the element with atomic number Z is to be placed is the unique value of R satisfying D(R-1) < Z <= D(R).

Once the row number R is determined, the column number is, from right to left, C = D(R) - Z + 1.

Example: Z=109. D(7) < Z <= D(8) = 120. C = 120 - 109 + 1 = 12. (End)