A103994 A129360 * A115361.

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

Offset: 1

Author

Gary W. Adamson, Apr 15 2007

Keywords

• tabl
• sign

Comments

Row sums = A104117: (1, 2, 0, 3, 0, 0, 0, 4, 0, 0, ...).

Examples

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

Links

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

Crossrefs

Column 1 is A209635 (Moebius transform of A104117).

Row sums are A104117.

Cf. A129360, A115361.

Programs

Mathematica

T[n_, k_] := If[Divisible[n, k], MoebiusMu[(n/k)/2^IntegerExponent[n/k, 2]], 0];
Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 14 2019 *)

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*Ti; for (n=1, nn, for (k=1, n, print1(Tp[n, k], ", ");); print(););}

PARI

T(n, k)={ if(n%k, 0, sumdiv(n/k, d, my(e=valuation(d, 2)); if(d==1<Andrew Howroyd, Aug 03 2018

Formula

A129360 * A115361 as infinite lower triangular matrices.

T(n,k) = A209635(n/k) for k | n, T(n,k) = 0 otherwise. - Andrew Howroyd, Aug 03 2018

Extensions

More terms from Michel Marcus, Mar 28 2015