A129360 A054525 * A115361.

1, 0, 1, -1, 0, 1, 0, 0, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1,1

Comments

Row sums = A209229 (1, 1, 0, 1, 0, 0, 0, 1, ...).

A129353 = the inverse Möbius transform of A115361.

Links

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

Formula

Moebius transform of A115361.

T(n,k) = A087003(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 03 2018

Example

First few rows of the triangle are:
   1;
   0,  1;
  -1,  0,  1;
   0,  0,  0,  1;
  -1,  0,  0,  0,  1;
   0, -1,  0,  0,  0,  1;
  -1,  0,  0,  0,  0,  0,  1;
   0,  0,  0,  0,  0,  0,  0,  1;
  ...

Prog

(PARI) tabl(nn) = {Tm = matrix(nn, nn, n, k, if (! (n % k), moebius(n/k), 0)); Tr = matrix(nn, nn, n, k, n--; k--; if ((n==k), 1, if (n==2*k+1, -1, 0))); Ti = Tr^(-1); Tp = Tm*Ti; for (n=1, nn, for (k=1, n, print1(Tp[n, k], ", "); ); print(); ); } \\ Michel Marcus, Mar 28 2015
(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)), 0))) } \\ Andrew Howroyd, Aug 03 2018

Crossrefs

Column 1 is A087003 (Moebius transform of A209229).

Row sums are A209229.

Cf. A054525, A115361, A129353, A001511, A103994, A129501.

Sequence in context: A288004 A102511 A266669 * A129372 A169591 A374646

Adjacent sequences: A129357 A129358 A129359 * A129361 A129362 A129363

Keyword

tabl,sign

Author

Gary W. Adamson, Apr 10 2007

Extensions

More terms from Michel Marcus, Mar 28 2015

Offset changed by Andrew Howroyd, Aug 03 2018

Status

approved