A129501 A103994 * A115361.

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, 0, 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

Offset

1,2

Comments

Row sums = A129502: (1, 3, 0, 6, 0, 0, 0, 10, 0, 0, ...).

Links

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

Formula

A103994 * A115361 as infinite lower triangular matrices.

T(n,k) = A317673(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 03 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;
   0,  0, -1,  0,  0,  0,  0,  0,  1;
  ...

Mathematica

b[n_] := Module[{e}, Sum[e = IntegerExponent[d, 2]; If[d == 2^e, MoebiusMu[n/d] Binomial[2 + e, 2], 0], {d, Divisors[n]}]];
T[n_, k_] := If[Divisible[n, k], b[n/k], 0];
Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 24 2019 *)

Prog

(PARI) T(n, k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<<e, moebius(n/(k*d))*binomial(2+e, 2), 0))) } \\ Andrew Howroyd, Aug 03 2018

Crossrefs

Column 1 is A317673 (Moebius transform of A129502).

Row sums are A129502.

Cf. A103994, A115361, A129360, A000217, A001511.

Sequence in context: A144409 A131257 A105806 * A129353 A174295 A158511

Adjacent sequences: A129498 A129499 A129500 * A129502 A129503 A129504

Keyword

tabl,sign

Author

Gary W. Adamson, Apr 17 2007

Extensions

Terms a(56) and beyond from Andrew Howroyd, Aug 03 2018

Status

approved