OFFSET
1,5
COMMENTS
For the number of compositions of n with relatively prime parts see A000740(n), giving the sums of row n of T.
EXAMPLE
The triangle T begins:
n\m 1 2 3 4 5 6 7 8 9 10 11 12 13 ... A000740(n)
1: 1
2: 0 1 1
3: 0 2 1 3
4: 0 2 3 1 6
5: 0 4 6 4 1 15
6: 0 2 9 10 5 1 27
7: 0 6 15 20 15 6 1 63
8: 0 4 18 34 35 21 7 1 120
9: 0 6 27 56 70 56 28 8 1 252
10: 0 4 30 80 125 126 84 36 9 1 495
11: 0 10 45 120 210 252 210 120 45 10 1 1023
12: 0 4 42 154 325 461 462 330 165 55 11 1 2010
13: 0 12 66 220 495 792 924 792 495 220 66 12 1 4095
...
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n = 5: The 15 compositions with relatively prime parts (with rising number of parts, and within like part numbers in lexicographic order) are
[[1, 4], [2, 3], [3, 2], [4, 1], [1, 1, 3], [1, 2, 2], [1, 3, 1], [2, 1, 2], [2, 2, 1], [3, 1, 1], [1, 1, 1, 2], [1, 1, 2, 1], [1, 2, 1, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1]].
The numbers for these compositions with m = 1, 2, 3, 4, 5 are 0, 4, 6, 4, 1, respectively.
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Jul 23 2022
STATUS
approved