A052173 Another version of the Catalan triangle A008315.

1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 3, 0, 2, 1, 0, 4, 0, 5, 0, 1, 0, 5, 0, 9, 0, 5, 1, 0, 6, 0, 14, 0, 14, 0, 1, 0, 7, 0, 20, 0, 28, 0, 14, 1, 0, 8, 0, 27, 0, 48, 0, 42, 0, 1, 0, 9, 0, 35, 0, 75, 0, 90, 0, 42, 1, 0, 10, 0, 44, 0, 110, 0, 165, 0, 132, 0, 1, 0, 11, 0, 54, 0, 154, 0, 275, 0, 297, 0

Offset: 0

Author

N. J. A. Sloane, Jan 26 2000

Keywords

• nonn
• easy
• tabl

Examples

			1;
1 0;
1 0 1;
1 0 2 0;
1 0 3 0 2;
1 0 4 0 5 0;
1 0 5 0 9 0 5;
...
		

Links

• R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
• W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, A Pascal rhombus, Fibonacci Quarterly, 35 (1997), 318-328.

Crossrefs

See A008315 (the main entry for this triangle) for more information.

Reflection of A053121.

Formula

a(n, k) = a(n-1, k-2)+a(n-1, k) with a(0, 0)=1 and a(n, k)=0 if k < 0 or k > n.

Extensions

More terms from Henry Bottomley, Aug 23 2001