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Search: id:A100452
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| A100452 |
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Triangle read by rows, based on array described below. |
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+0
6
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| 1, 3, 4, 7, 8, 9, 13, 14, 15, 16, 19, 20, 21, 24, 25, 27, 28, 30, 32, 35, 36, 39, 40, 42, 44, 45, 48, 49, 49, 50, 51, 52, 55, 60, 63, 64, 63, 64, 66, 68, 70, 72, 77, 80, 81, 79, 80, 81, 84, 85, 90, 91, 96, 99, 100, 91, 92, 93, 96, 100, 102, 105, 112, 117, 120
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Form an array a(m,n) (n >= 1, 1 <= m <= n) by: a(1,n) = n^2 for all n; a(m+1,n) = (n-m)*floor( (a(m,n)-1)/(n-m) ) for 1 <= m <= n-1.
The interesting property of this array is that the main diagonal gives A000960.
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REFERENCES
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H. Killingbergtro and C. U. Jensen, Problem 116, Nord. Mat. Tidskr. 5 (1957), 160-161.
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EXAMPLE
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Array begins:
1 4 9 16 25 36 49 64 81 100 ...
* 3 8 15 24 35 48 63 80 99 ...
* * 7 14 21 32 45 60 77 96 ...
* * * 13 20 30 44 55 72 91 ...
* * * * 19 28 42 52 70 90 ...
and triangle begins:
1
3 4
7 8 9
13 14 15 16
19 20 21 24 25
27 28 30 32 35 36
...
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CROSSREFS
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Cf. A000960, A100453. Row 1 = squares, row 2 = squares - 1, row 3 = A100451. Column sums give A100454.
See also A100461.
Sequence in context: A047545 A105941 A110133 this_sequence A004201 A109054 A129142
Adjacent sequences: A100449 A100450 A100451 this_sequence A100453 A100454 A100455
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KEYWORD
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nonn,tabl,nice
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AUTHOR
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njas, Nov 22 2004
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