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

1,5

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,...).

Links

Table of n, a(n) for n=1..91.

Formula

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

Example

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;
...

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 *)

Crossrefs

Cf. A101688, A129819, A168317, A168318.

Sequence in context: A170975 A284313 A169975 * A305259 A029370 A369572

Adjacent sequences: A168313 A168314 A168315 * A168317 A168318 A168319

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 22 2009

Extensions

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

Status

approved