|
| |
|
|
A054525
|
|
Triangle T(n,k): T(n,k) = mu(n/k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n).
|
|
94
|
|
|
|
1, -1, 1, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 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, 0, 1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
A051731 = the inverse of this triangle = A129372 * A115361. - Gary W. Adamson, Apr 15 2007
If a column T(n,0)=0 is added, these are the coefficients of the necklace polynomials multiplied by n [Moree,Metropolis]. [From R. J. Mathar, Nov 11 2008]
|
|
|
LINKS
|
Table of n, a(n) for n=1..93.
Pieter Moree, The formal series Witt transform, Discr. Math. 295 (2005), 143-160. [From R. J. Mathar, Nov 11 2008]
N. Metropolis, G.-C. Rota, Witt vectors and the algebra of necklaces, Adv. Math. 50 (1983), 95-125. [From R. J. Mathar, Nov 11 2008]
|
|
|
FORMULA
|
Matrix inverse of triangle A051731, where A051731(n, k) = 1 if k|n, 0 otherwise. - Paul D. Hanna, Jan 09 2006
Equals = A129360 * A115369 as infinite lower triangular matrices. - Gary W. Adamson, Apr 15 2007
|
|
|
EXAMPLE
|
Triangle begins:
1;
-1,1;
-1,0,1;
0,-1,0,1;
-1,0,0,0,1;
1,-1,-1,0,0,1;
-1,0,0,0,0,0,1;
0,0,0,-1,0,0,0,1; ...
Matrix inverse is triangle A051731:
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; ...
|
|
|
MAPLE
|
A054525 := proc(n, k)
if n mod k = 0 then
numtheory[mobius](n/k) ;
else
0 ;
end if;
end proc: # R. J. Mathar, Oct 21 2012
|
|
|
CROSSREFS
|
Cf. A054521.
Cf. A051731.
Cf. A129360, A115369.
Sequence in context: A115952 A115524 A117198 * A174852 A065333 A127972
Adjacent sequences: A054522 A054523 A054524 * A054526 A054527 A054528
|
|
|
KEYWORD
|
sign,tabl
|
|
|
AUTHOR
|
N. J. A. Sloane, Apr 09 2000
|
|
|
STATUS
|
approved
|
| |
|
|
