A307239 Analog of Pascal's triangle, with A007947 applied to each sum.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 5, 2, 5, 2, 1, 1, 3, 7, 7, 7, 7, 3, 1, 1, 2, 10, 14, 14, 14, 10, 2, 1, 1, 3, 6, 6, 14, 14, 6, 6, 3, 1, 1, 2, 3, 6, 10, 14, 10, 6, 3, 2, 1, 1, 3, 5, 3, 2, 6, 6, 2, 3, 5, 3, 1, 1, 2, 2, 2, 5, 2, 6, 2, 5, 2, 2, 2, 1

Offset

0,5

Comments

The parity of the terms in this triangle is the same as in Pascal's triangle (A007318). As a consequence, the number of odd terms in row n is A001316(n).

The distribution of the terms different from 2 in the triangle evokes Sierpinski's triangle; this is also the case for terms that are multiples of 3 (see illustrations in Links section).

Links

Table of n, a(n) for n=0..90.

Rémy Sigrist, Colored representation of the first 1500 rows (where the color is function of log(T(n,k)))

Rémy Sigrist, Representation of the 2's in the first 1500 rows (black pixels correspond to 2's)

Rémy Sigrist, Representation of the multiples of 3 in the first 1500 rows (black pixels correspond to multiples of 3)

Example

Triangle begins:
  0:                       1
  1:                     1   1
  2:                   1   2   1
  3:                 1   3   3   1
  4:               1   2   6   2   1
  5:             1   3   2   2   3   1
  6:           1   2   5   2   5   2   1
  7:         1   3   7   7   7   7   3   1
  8:       1   2  10  14  14  14  10   2   1
  9:     1   3   6   6  14  14   6   6   3   1
  ...

Prog

(PARI) rad(n) = my (p=factor(n)[, 1]~); prod(i=1, #p, p[i])
{ for (r=0, 12, row = vector(r+1, k, if ( k==1||k==r+1, 1, rad(row[k-1]+row[k]))); for (c=1, #row, print1 (row[c] ", "))) }

Crossrefs

Cf. A001316, A007318, A007947, A080396, A307356 (number of 2's in rows).

Sequence in context: A132422 A065133 A343033 * A204087 A080381 A080396

Adjacent sequences: A307236 A307237 A307238 * A307240 A307241 A307242

Keyword

nonn,tabl

Author

Rémy Sigrist, Apr 01 2019

Status

approved