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

2,3

Comments

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).

Links

Table of n, a(n) for n=2..72.

Rémy Sigrist, PARI program

Index entries for triangles and arrays related to Pascal's triangle

Example

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.

Prog

(PARI) See Links section.

Crossrefs

Cf. A000217, A007318, A360653, A360655.

Sequence in context: A318772 A317496 A304236 * A145063 A202851 A007650

Adjacent sequences: A360651 A360652 A360653 * A360655 A360656 A360657

Keyword

nonn,tabf

Author

Rémy Sigrist, Feb 15 2023

Status

approved