A168317 -id:A168317 - cp's OEIS frontend

A168318 Triangle read by rows, A168316 * its diagonalized eigensequence, A168317.

1, 0, 1, 0, 2, 1, 0, 1, 2, 3, 0, 1, 3, 6, 6, 0, 0, 2, 9, 12, 16, 0, 0, 2, 12, 18, 32, 39, 0, 0, 1, 9, 24, 48, 78, 103, 0, 0, 1, 9, 30, 64, 117, 206, 263, 0, 0, 0, 6, 24, 80, 156, 309, 526, 690, 0, 0, 0, 6, 24, 96, 195, 412, 789, 1380, 1791

Offset: 1

Gary W. Adamson, Nov 22 2009

Row sums = A168317: (1, 1, 3, 6, 16, 39, 103, 263,...).
Rightmost diagonal = A168317 prefaced with a 1.
Sum of n-th row terms = rightmost term of next row.

			First few rows of the triangle =
1;
0, 1;
0, 2, 1;
0, 1, 2, 3;
0, 1, 3, 6, 6;
0, 0, 2, 9, 12, 16;
0, 0, 2, 12, 18, 32, 39;
0, 0, 1, 9, 24, 48, 78, 103;
0, 0, 1, 9, 30, 64, 117, 206, 263;
0, 0, 0, 6, 24, 80, 156, 309, 526, 690;
0, 0, 0, 6, 24, 96, 195, 412, 789, 1380, 1791;
0, 0, 0, 3, 18, 80, 234, 515, 1052, 2070, 3582, 4693;
0, 0, 0, 3, 18, 80, 273, 618, 1315, 2760, 5373, 9386, 12247;
0, 0, 0, 0, 12, 64, 234, 721, 1578, 3450, 7164, 14079, 24494, 32073;
...

Cf. A168316, A168317

Triangle read by rows, M*Q. M = A168316, Q = an infinite lower triangular matrix
with A168317 prefaced with a 1; (1, 1, 1, 3, 6, 16, 39, 103,...) as the right
diagonal and the rest zeros.

A168316 Triangle read by rows, square of triangle A101688.

Original entry on oeis.org

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

Gary W. Adamson, Nov 22 2009

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,...).

			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;
...

Cf. A101688, A129819, A168317, A168318.

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 *)

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

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

cp's OEIS Frontend

A168318 Triangle read by rows, A168316 * its diagonalized eigensequence, A168317.

Views

Author

Keywords

Comments

Examples

Crossrefs

Formula