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A066099
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Triangle read by rows, in which row n lists the compositions of n in reverse lexicographic order.
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35
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0, 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, 5, 4, 1, 3, 2, 3, 1, 1, 2, 3, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 4, 1, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 4, 1, 1, 3, 3, 3, 2, 1, 3, 1, 2, 3, 1, 1, 1, 2, 4, 2, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
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LINKS
| 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, 1972 [alternative scanned copy].
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EXAMPLE
| 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
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CROSSREFS
| 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: A084580 A171850 A087782 * A006375 A184441 A172279
Adjacent sequences: A066096 A066097 A066098 * A066100 A066101 A066102
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KEYWORD
| easy,nice,nonn,tabf
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Dec 30 2001
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EXTENSIONS
| Edited with additional terms by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 06 2006
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