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
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; ...
Programs
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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
Comments