A134543 Triangle read by rows: T(n,k) = Sum_{i=k..n} (i+1-k)*A134541(n,i).

1, 2, 1, 4, 3, 1, 6, 5, 3, 1, 10, 9, 6, 3, 1, 12, 11, 9, 6, 3, 1, 18, 17, 14, 10, 6, 3, 1, 22, 21, 18, 14, 10, 6, 3, 1, 28, 27, 24, 20, 15, 10, 6, 3, 1, 32, 31, 29, 25, 20, 15, 10, 6, 3, 1, 42, 41, 38, 33, 27, 21, 15, 10, 6, 3, 1, 46, 45, 42, 38, 33, 27, 21, 15, 10, 6, 3, 1

Offset

1,2

Comments

Conjecture: row terms starting from the right tend to the triangular series.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Formula

Equals A134542 * A000012 as infinite lower triangular matrices.

T(n,k) = Sum_{i=k..n} A134542(n,i).

Example

First few rows of the triangle:
   1;
   2,  1;
   4,  3,  1;
   6,  5,  3,  1;
  10,  9,  6,  3,  1;
  12, 11,  9,  6,  3,  1;
  18, 17, 14, 10,  6,  3,  1;
  22, 21, 18, 14, 10,  6,  3,  1;
  28, 27, 24, 20, 15, 10,  6,  3,  1;
  ...

Prog

(PARI) \\ here b(n) is A002321.
b(n) = sum(i=1, n, moebius(i))
T(n, k) = sum(i=k, n, (i+1-k)*b(n\i))

Crossrefs

Row sums are A015631.

Column 1 is A002088.

Cf. A002321, A134541, A134542.

Sequence in context: A093682 A344767 A187883 * A305540 A197871 A093010

Adjacent sequences: A134540 A134541 A134542 * A134544 A134545 A134546

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 31 2007

Extensions

New name and a(56) onwards from Andrew Howroyd, Sep 20 2025

Status

approved