A360653 -id:A360653 - cp's OEIS frontend

A360654 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n.

1, 1, 3, 1, 6, 1, 10, 1, 4, 15, 1, 21, 1, 28, 1, 36, 1, 5, 10, 45, 1, 55, 1, 66, 1, 78, 1, 91, 1, 6, 20, 105, 1, 120, 1, 136, 1, 153, 1, 171, 1, 15, 190, 1, 7, 35, 210, 1, 231, 1, 253, 1, 276, 1, 300, 1, 325, 1, 351, 1, 8, 56, 378, 1, 406, 1, 435, 1, 465, 1, 496

Offset: 2

Rémy Sigrist, Feb 15 2023

In other words, the n-th rows lists the numbers horizontally adjacent to n in Pascal's triangle (A007318).

The n-th contains 1 and A000217(n-1).

			Table begins:
  n   n-th row
  --  ------------
   2  1
   3  1, 3
   4  1, 6
   5  1, 10
   6  1, 4, 15
   7  1, 21
   8  1, 28
   9  1, 36
  10  1, 5, 10, 45
  11  1, 55
  12  1, 66
.
For n = 6:
    Pascal's triangle begins as follows:
                     1
                   1   1
                 1   2   1
               1   3   3   1
             1   4   6   4   1
           1   5  10  10   5   1
         1   6  15  20  15   6   1
    we find the value 6 in row 4 between 4 and 4, and in row 6 between 1 and 15,
    so the 6th row contains 1, 4 and 15.

Rémy Sigrist, PARI program
Index entries for triangles and arrays related to Pascal's triangle

Cf. A000217, A007318, A360653, A360655.

PARI
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See Links section.
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A360655 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m+1, k) such that binomial(m, k) = n.

Original entry on oeis.org

3, 4, 6, 5, 10, 6, 15, 7, 10, 21, 8, 28, 9, 36, 10, 45, 11, 15, 20, 55, 12, 66, 13, 78, 14, 91, 15, 105, 16, 21, 35, 120, 17, 136, 18, 153, 19, 171, 20, 190, 21, 35, 210, 22, 28, 56, 231, 23, 253, 24, 276, 25, 300, 26, 325, 27, 351, 28, 378, 29, 36, 84, 406, 30, 435

Offset: 2

Rémy Sigrist, Feb 15 2023

In other words, the n-th rows lists the numbers that appear directly below n in Pascal's triangle (A007318).

The n-th row starts with n+1.

			Table begins:
  n   n-th row
  --  --------------
   2  3
   3  4, 6
   4  5, 10
   5  6, 15
   6  7, 10, 21
   7  8, 28
   8  9, 36
   9  10, 45
  10  11, 15, 20, 55
  11  12, 66
  12  13, 78
.
For n = 6:
    Pascal's triangle begins:
                      1
                    1   1
                  1   2   1
                1   3   3   1
              1   4   6   4   1
            1   5  10  10   5   1
          1   6  15  20  15   6   1
        1   7  21  35  35  21   7   1
    the value 6 appears in row 3 above 10, and in row 6 above 7 and 21,
    so the 6th row contains 7, 10 and 21.

Rémy Sigrist, PARI program
Index entries for triangles and arrays related to Pascal's triangle

Cf. A007318, A360653, A360654.

PARI
```
See Links section.
```

cp's OEIS Frontend

A360654 Irregular table read by rows; for n > 1, the n-th row lists the numbers of the form binomial(m, k-1) such that binomial(m, k) = n.

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