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Search: id:A105552
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| A105552 |
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An alternative construction for A047970 (1 2 5 14 43 144 ...). |
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+0
4
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| 1, 2, 4, 1, 7, 5, 2, 11, 14, 12, 5, 1, 16, 30, 39, 32, 18, 7, 2, 22, 55, 95, 113, 101, 71, 41, 18, 6, 1, 29, 91, 195, 299, 357, 350, 292, 207, 126, 64, 27, 9, 2, 37, 140, 357, 664, 978, 1204, 1283, 1198, 992, 731, 482, 284, 148, 66, 25, 7, 1
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Column sums are A047970. Row sums are A000079. Using the Gaussian polynomials, as illustrated in A083906, the columns can be expanded to display more detail; for example, column five is a summation by row of
1.2.3.4.1
..2.6.6
..2.6.4
..1.3.1
....1
Each cell in the array counts a subset of the Quet numbers, A055932. In the above expansion, the first "6" counts the Quet numbers 360,540,600,1350,1500 and 2250 which encode the prime signatures for the symmetric group over 3 symbols. The distribution of the least prime signatures is described in A083480.
Each diagonal can be decomposed into p(n) sequences. For example,
A086602 = 2 12 39 95 195 ... is the sum of
A000330 = 1 5 14 30 55 ... plus
A001296 = 1 7 25 65 140 ...
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EXAMPLE
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If viewed as an array with A033638(n) entries per column the sequence would begin
1
..2
....4
....1..7
.......5..11
.......2..14..16
..........12..30..22
...........5..39..55..29
...........1..32..95..91..37
..............18.113.195.140
...............7.101.299.357
...............2
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CROSSREFS
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Cf. A047969, A047970, A055932, A057335, A083480, A083906, A089349, A033638.
Diagonals in order of appearance are A000124, A000330, A086602, A089574, A107600, A107601, A109125, ...
Adjacent sequences: A105549 A105550 A105551 this_sequence A105553 A105554 A105555
Sequence in context: A089087 A143350 A119303 this_sequence A112852 A121531 A127554
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KEYWORD
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more,nonn,uned
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), May 03 2005
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