A391991 Triangle read by rows: T(n,k) = number of digits in decimal representation of binomial(n,k), 0<=k<=n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 1, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 2, 2, 1

Offset

0,18

Links

Table of n, a(n) for n=0..104.

Wikipedia, Logarithmically concave sequence

Formula

T(n,k) = A055642(A007318(n,k)).

T(n,k) = T(n,n-k).

Example

Triangle begins:
  1;
  1, 1;
  1, 1, 1;
  1, 1, 1, 1;
  1, 1, 1, 1, 1;
  1, 1, 2, 2, 1, 1;
  1, 1, 2, 2, 2, 1, 1;
  1, 1, 2, 2, 2, 2, 1, 1;
  1, 1, 2, 2, 2, 2, 2, 1, 1;
  1, 1, 2, 2, 3, 3, 2, 2, 1, 1;
  1, 2, 2, 3, 3, 3, 3, 3, 2, 2, 1;
  1, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 1;
  1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1;
  1, 2, 2, 3, 3, 4, 4, 4, 4, 3, 3, 2, 2, 1;
  1, 2, 2, 3, 4, 4, 4, 4, 4, 4, 4, 3, 2, 2, 1;
  ...

Prog

(PARI) T(n, k) = length(digits(binomial(n, k)));

Crossrefs

Cf. A391992 (central terms).

Cf. A007318, A055642, A101598.

Sequence in context: A015716 A308884 A101598 * A342461 A157129 A101615

Adjacent sequences: A391988 A391989 A391990 * A391992 A391993 A391994

Keyword

nonn,tabl,easy,base

Author

Seiichi Manyama, Dec 26 2025

Status

approved