OFFSET
0,5
LINKS
M. F. Hasler, A050186, rows 0..50, Sep 27 2018
M. F. Hasler, A050186, rows 0..100, Sep 27 2018
M. F. Hasler, A050186, rows 0..200, Sep 27 2018
N. J. A. Sloane, Transforms
FORMULA
MOEBIUS transform of A007318 Pascal's Triangle.
If rows n > 1 are divided by n, this yields the triangle A051168, which equals A245558 surrounded by 0's (except for initial terms). This differs from A011847 from row n = 9 on. - M. F. Hasler, Sep 29 2018
EXAMPLE
For example, T(4,2) counts 1100,1001,0011,0110; T(2,1) counts 10, 01 (hence also counts 1010, 0101).
Rows:
1;
1, 1;
0, 2, 0;
0, 3, 3, 0;
0, 4, 4, 4, 0;
0, 5, 10, 10, 5, 0;
MATHEMATICA
T[n_, k_] := If[n == 0, 1, DivisorSum[GCD[k, n], MoebiusMu[#] Binomial[n/#, k/#]&]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jul 16 2022 *)
PROG
(PARI) A050186(n, k)=sumdiv(gcd(n+!n, k), d, moebius(d)*binomial(n/d, k/d)) \\ M. F. Hasler, Sep 27 2018
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved