A129353 Triangle read by rows: A051731 * A115361 as infinite lower triangular matrices.

1, 2, 1, 1, 0, 1, 3, 2, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 4, 3, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 2, 3, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,2

Comments

The inverse Moebius transform of the first column of A115361 which is A209229 gives the first column of this sequence.

Links

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

Formula

T(n,k) = A001511(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 04 2018

Example

First few rows of the triangle are:
  1;
  2, 1;
  1, 0, 1;
  3, 2, 0, 1;
  1, 0, 0, 0, 1;
  2, 1, 2, 0, 0, 1;
  1, 0, 0, 0, 0, 0, 1;
  4, 3, 0, 2, 0, 0, 0, 1;
  ...

Maple

A129353 := proc(n, k)
        add( A051731(n, j)*A115361(j-1, k-1), j=k..n) ;
end proc: # R. J. Mathar, Jul 14 2012

Mathematica

T[n_, k_] := If[Mod[n, k] != 0, 0, 1 + IntegerExponent[n/k, 2]];
Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* Jean-François Alcover, Apr 08 2020, from PARI *)

Prog

(PARI) T(n, k)={if(n%k, 0, 1 + valuation(n/k, 2))} \\ Andrew Howroyd, Aug 04 2018

Crossrefs

Column 1 is A001511.

Row sums are A129628 (inverse Moebius transform of A001511).

Cf. A051731, A115361.

Sequence in context: A131257 A105806 A129501 * A174295 A158511 A092921

Adjacent sequences: A129350 A129351 A129352 * A129354 A129355 A129356

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 10 2007

Status

approved