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

0,9

Links

Table of n, a(n) for n=0..89.

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.

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.

Example

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;
...

Crossrefs

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

Reflection of A053121.

Sequence in context: A104477 A224928 A308066 * A177825 A175790 A124305

Adjacent sequences: A052170 A052171 A052172 * A052174 A052175 A052176

Keyword

nonn,easy,tabl

Author

N. J. A. Sloane, Jan 26 2000

Extensions

More terms from Henry Bottomley, Aug 23 2001

Status

approved