A158902 Triangle read by rows: the matrix product A051731 * A158821.

1, 2, 1, 3, 0, 1, 5, 1, 0, 1, 5, 0, 0, 0, 1, 9, 1, 1, 0, 0, 1, 7, 0, 0, 0, 0, 0, 1, 12, 1, 0, 1, 0, 0, 0, 1, 11, 0, 1, 0, 0, 0, 0, 0, 1, 15, 1, 0, 0, 1, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 23, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Gary W. Adamson and Mats Granvik, Mar 29 2009

Keywords

• nonn
• tabl

Examples

			First few rows of the triangle =
1;
2, 1;
3, 0, 1;
5, 1, 0, 1;
5, 0, 0, 0, 1;
9, 1, 1, 0, 0, 1;
7, 0, 0, 0, 0, 0, 1;
12, 1, 0, 1, 0, 0, 0, 1
11, 0, 1, 0, 0, 0, 0, 0, 1;
15, 1, 0, 0, 1, 0, 0, 0, 0, 1;
11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
23, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1;
13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
21, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1;
...
		

Crossrefs

Cf. A158821, A051731, A158901, A000203 (row sums).

Programs

Maple

A158902 := proc(n,k)
    add( A051731(n,j)*A158821(j-1,k-1),j=k..n) ;
end proc:
seq(seq(A158902(n,k),k=1..n),n=1..12) ; # R. J. Mathar, Jan 08 2015

Mathematica

m = 12; (* number of rows *)
T1[n_, k_] := Boole[Mod[n, k] == 0];
T2[n_, k_] := Which[n == k, 1, k == 1, n-1, True, 0];
T = Array[T1, {m, m}].Array[T2, {m, m}];
Table[T[[n, k]], {n, m}, {k, n}] // Flatten (* Jean-François Alcover, Feb 01 2023 *)

Formula

T(n,n) = 1.

T(n,1) = A158901(n).

Extensions

Wrong A-number in definition corrected by Robert Israel, Jan 08 2015