I have here left out the indices of the elements for easier typing but hopefully this can still be understood.

Shift down the elements in matrix two steps to get matrix .

Add two diagonals of ones to the main diagonal (where row index = column index) and to the diagonal below (where row index = column index + 1) in matrix to get matrix .

Change the sign of all the elements below the main diagonal in matrix so that you get matrix .

Calculate the matrix inverse of matrix to get matrix

Iterate by replacing matrix with matrix .

Matrix should then converge to the Motzkin numbers in all columns.

Keywords: Matrix inversion, Motzkin numbers, iteration.

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