A168316 Triangle read by rows, square of triangle A101688.

1, 0, 1, 0, 2, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 0, 0, 2, 3, 2, 1, 0, 0, 2, 4, 3, 2, 1, 0, 0, 1, 3, 4, 3, 2, 1, 0, 0, 1, 3, 5, 4, 3, 2, 1, 0, 0, 0, 2, 4, 5, 4, 3, 2, 1, 0, 0, 0, 2, 4, 6, 5, 4, 3, 2, 1, 0, 0, 0, 1, 3, 5, 6, 5, 4, 3, 2, 1, 0, 0, 0, 1, 3, 5, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Gary W. Adamson, Nov 22 2009

Keywords

• nonn
• tabl

Comments

Row sums = A129819 starting (1, 1, 3, 4, 7, 8, 12,...).

Eigensequence of the triangle = A168317: (1, 1, 3, 6, 16, 39, 103, 263, 690,...).

Examples

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

Crossrefs

Cf. A101688, A129819, A168317, A168318.

Programs

Mathematica

rows = 15; A = Array[If[#1 <= #2, 1, 0]&, {rows, rows}];
M = Table[PadRight[Table[A[[i-j+1, j]], {j, 1, i}], rows], {i, 1, rows}];
M2 = MatrixPower[M, 2];
Table[M2[[i, j]], {i, 1, rows}, {j, 1, i}] // Flatten (* Jean-François Alcover, May 04 2017 *)

Formula

Triangle read by rows, (A101688)^2, as an infinite lower triangular matrix.

Extensions

Missing row inserted by Jean-François Alcover, May 04 2017