0,3

This is the standard ordering for compositions in this database; it is similar to the Mathematica ordering for partitions (A080577). Other composition orderings include A124734 (similar to the Abramowitz & Stegun ordering for partitions, A036036) and A108244 (similar to the Maple partition ordering, A080576).

Factorize each term in A057335; sequence records the values of the resulting exponents. It also runs through all possible permutations of multiset digits.

This can be regarded as a table in two ways: with each composition as a row, or with the compositions of each integer as a row. The first way has A000120 as row lengths (except for the initial 0) and A070939 as row sums; the second has A001792 as row lengths (again, except for the initial 0), and A001788 as row sums. - Franklin T. Adams-Watters, Nov 06 2006

This sequence includes every finite sequence of positive integers. - Franklin T. Adams-Watters, Nov 06 2006

Compositions (or ordered partitions) are also generated in sequence A101211. - Alford Arnold (Alford1940(AT)aol.com), Dec 12 2006

Franklin T. Adams-Watters, Table of n, a(n) for n = 0..5120 (through compositions of 10)

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

The 25th row is associated with the Quet number 162 = 2^1 *

3^3 * 5^1 so the exponents for the ordered prime signature form the

vector (1,3,1). Following the method described in A108730 we subtract

one from each cell yielding (0,2,0) which gives the number of zeros

following each 1 in 11001 (the binary representation of the number 25).

- Alford Arnold (Alford1940(AT)aol.com), Mar 05 2006

A057335 begins 1 2 4 6 8 12 18 30 16 24 36 ... so we can write

1 2 1 3 2 1 1 4 3 2 2 1 1 1 1 ...

. . 1 . 1 2 1 . 1 2 1 3 2 1 1 ...

. . . . . . 1 . . . 1 . 1 2 1 ...

. . . . . . . . . . . . . . 1 ...

- and the columns here gives the rows of the triangle, which begins

1

2; 1 1

3; 2 1; 1 2; 1 1 1

4; 3 1; 2 2; 2 1 1; 1 3; 1 2 1; 1 1 2; 1 1 1 1

Cf. A065120, A057335, A055932. Other versions of this triangle are in A108244, A108730, and A124734.

Cf. A096903, A000120, A070939, A001792, A001788.

Cf. A005811 A101211.

Sequence in context: A030305 A084580 A087782 this_sequence A006375 A136622 A025474

Adjacent sequences: A066096 A066097 A066098 this_sequence A066100 A066101 A066102

easy,nice,nonn,tabf

Alford Arnold (Alford1940(AT)aol.com), Dec 30 2001

Edited with additional terms by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006