A234305 Irregular triangle read by rows. Theoretical distribution of electrons based on the Janet's sequence A167268.

1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 5, 2, 2, 6, 2, 2, 6, 1, 2, 2, 6, 2, 2, 2, 6, 2, 1, 2, 2, 6, 2, 2, 2, 2, 6, 2, 3, 2, 2, 6, 2, 4, 2, 2, 6, 2, 5, 2, 2, 6, 2, 6, 2, 2, 6, 2, 6, 1, 2, 2, 6, 2, 6, 2, 2, 2, 6, 2, 6, 2, 1, 2, 2, 6, 2, 6, 2, 2, 2, 2, 6, 2, 6, 2, 3, 2, 2, 6, 2, 6, 2, 4

Offset

1,2

Comments

a(n) is not A173642, a compact Bohr-Stoner model (1924), modified by Charles Janet in 1930. The good distribution is A168208.

Only sequences N16(n) in A234398 are used:

N16(1)= 1 followed by 2's = A040000,

N16(2)= 1, 2, 3, 4, 5, followed by 6's = A101272,

N16(3)= 1 to 9, followed by 10's,

N16(4)= 1 to 13, followed by 14's, etc.

The distribution by rows are in the example.

The N16(n)'s are respectively on columns (hence triangle T)

1, 2, 4, 6, 9, 12, 16, 20, 25, 30, 36, A002620(n+2)

3, 5, 8, 11, 15, 19, 24, 29, 35, A024206(n+2)

7, 10, 14, 18, 23, 28, 34, A014616(n+3)

13, 17, 22, 27, 33, A004116(n+4)

21, 26, 32,

31, etc.

See A163255.

Antidiagonals give the natural numbers A000027, like rows sums in the example.

A033638=1, 1, 2, 3, 5, 7,... is upon the triangle T.

Links

Table of n, a(n) for n=1..102.

Example

1,      H
2,       He
2, 1,    Li
2, 2,    Be
2, 2, 1,
2, 2, 2,
2, 2, 3,
2, 2, 4,
2, 2, 5,
2, 2, 6,
2, 2, 6, 1,
2, 2, 6, 2,
2, 2, 6, 2, 1,
2, 2, 6, 2, 2,
2, 2, 6, 2, 3,
2, 2, 6, 2, 4,
2, 2, 6, 2, 5,
2, 2, 6, 2, 6,
2, 2, 6, 2, 6, 1,
2, 2, 6, 2, 6, 2,
2, 2, 6, 2, 6, 2, 1,
2, 2, 6, 2, 6, 2, 2,
2, 2, 6, 2, 6, 2, 3, etc.

Crossrefs

Cf. A002061, A002522 (or A160457), A014206, A059100, diagonals of the triangle T. A004526.

Sequence in context: A275437 A169695 A173642 * A339701 A304094 A259527

Adjacent sequences: A234302 A234303 A234304 * A234306 A234307 A234308

Keyword

nonn,tabf,uned

Author

Paul Curtz, Jan 02 2014

Status

approved