A158906 Triangle read by rows: the matrix product A158821 * A051731.

1, 2, 1, 3, 0, 1, 4, 1, 0, 1, 5, 0, 0, 0, 1, 6, 1, 1, 0, 0, 1, 7, 0, 0, 0, 0, 0, 1, 8, 1, 0, 1, 0, 0, 0, 1, 9, 0, 1, 0, 0, 0, 0, 0, 1, 10, 1, 0, 0, 1, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1

Offset

1,2

Links

Table of n, a(n) for n=1..78.

Formula

Triangle read by rows, A158821 * A051731, where A051731 = the inverse Mobius transform.

T(n,k) = A051731(n,k) if k>1.

T(n,1) = n.

Example

First few rows of the triangle =
1;
2, 1;
3, 0, 1;
4, 1, 0, 1;
5, 0, 0, 0, 1;
6, 1, 1, 0, 0, 1;
7, 0, 0, 0, 0, 0, 1;
8, 1, 0, 1, 0, 0, 0, 1;
9, 0, 1, 0, 0, 0, 0, 0, 1;
10, 1, 0, 0, 1, 0, 0, 0, 0, 1;
11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
12, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1;
13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
...

Maple

N:= 20: # to get the first N rows
M1:= Matrix(N, N, shape = triangular[lower]);
M1[.., 1] := Vector([$0..N-1]);
M1:= M1 + LinearAlgebra:-IdentityMatrix(N);
M2:= Matrix(N, N, shape=triangular[lower], (i, j) -> charfcn[0](i mod j));
M:= M1 . M2;
seq(seq(M[i, j], j=1..i), i=1..N); # Robert Israel, Jan 08 2015

Crossrefs

Cf. A158821, A051731, A158907 (row sums).

Sequence in context: A141673 A127094 A221642 * A309229 A143239 A158951

Adjacent sequences: A158903 A158904 A158905 * A158907 A158908 A158909

Keyword

nonn,tabl

Author

Gary W. Adamson and Mats Granvik, Mar 29 2009

Status

approved