A177457 Triangle read by rows; union of A007318 and A112467.

0, 1, 1, -1, 1, 1, 0, 1, -1, 1, 1, 1, 2, -1, 1, -1, 1, 1, 2, 3, 0, 3, -2, 1, -1, 1, 1, 3, 4, 2, 6, -2, 4, -3, 1, -1, 1, 1, 4, 5, 5, 10, 0, 10, -5, 5, -4, 1, -1, 1, 1, 5, 6, 9, 15, 5, 20, -5, 15, -9, 6, -5, 1, -1, 1, 1, 6, 7, 14, 21, 14, 35, 0, 35, -14, 21, -14, 7, -6, 1, -1, 1, 1, 7, 8, 20, 28

Offset: 1

Author

Mark Dols, May 09 2010

Keywords

• tabf
• sign

Examples

			Triangle begins:
                 0
              1  1 -1
           1  1  0  1 -1
        1  1  1  2 -1  1 -1
     1  1  2  3  0  3 -2  1 -1
  1  1  3  4  2  6 -2  4 -3  1 -1
		

Crossrefs

Cf. A007318, A112467.

Programs

MATLAB

function a = A177457( max_row )
    a = [0 1 1 -1];
    for n = 3:max_row
        r = [0 0 a(end-((n-2)*2):end) 0 0];
        a = [a r(1:end-2)+r(3:end)];
    end
end % Thomas Scheuerle, Feb 02 2023

Formula

T(n, k) = T(n-1, k-1) + T(n-1, k+1), for n > 2 and T(n, k) = 0 for negative k or k > 2*n-1. - Thomas Scheuerle, Feb 02 2023

Extensions

More terms from Thomas Scheuerle, Feb 02 2023