A356027 Triangle T(n, m) read by rows of numbers of compositions of n into m relatively prime parts, for n >= 1, and m = 1, 2, ..., n.

1, 0, 1, 0, 2, 1, 0, 2, 3, 1, 0, 4, 6, 4, 1, 0, 2, 9, 10, 5, 1, 0, 6, 15, 20, 15, 6, 1, 0, 4, 18, 34, 35, 21, 7, 1, 0, 6, 27, 56, 70, 56, 28, 8, 1, 0, 4, 30, 80, 125, 126, 84, 36, 9, 1, 0, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1, 0, 4, 42, 154, 325, 461, 462, 330, 165, 55, 11, 1, 0, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1

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.

Links

Table of n, a(n) for n=1..91.

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
...
-----------------------------------------------------------------
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

Cf. A000740, A000837, A007318(n-1,m-1) (for compositions of n >= 1 with m parts, for m = 1..n), A282750.

Sequence in context: A131084 A143067 A219605 * A123949 A236358 A144082

Adjacent sequences: A356024 A356025 A356026 * A356028 A356029 A356030

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Jul 23 2022

Status

approved