A108036 Triangle read by rows: the triangle in A108035 surrounded by a border of 0's.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 3, 3, 3, 0, 0, 5, 5, 5, 5, 0, 0, 8, 8, 8, 8, 8, 0, 0, 13, 13, 13, 13, 13, 13, 0, 0, 21, 21, 21, 21, 21, 21, 21, 0, 0, 34, 34, 34, 34, 34, 34, 34, 34, 0, 0, 55, 55, 55, 55, 55, 55, 55, 55, 55, 0, 0, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 0, 0, 144, 144, 144, 144

Offset: 0

Author

N. J. A. Sloane, Jun 01 2005

Keywords

• nonn
• tabl

Examples

			0; 0,0; 0,1,0; 0,2,2,0; 0,3,3,3,0; 0,5,5,5,5,0; ...
		

Crossrefs

Cf. A039913, A108035.

Programs

Python

from math import isqrt
from sympy import fibonacci
def A108036(n): return 0 if 0<=(k:=n+1<<1)-(r:=(m:=isqrt(k))*(m+1))<=2 or n<=1 else int(fibonacci(m-(k<=r))) # Chai Wah Wu, Nov 07 2024

Formula

G.f.: x*y*(1+x+y)/((1-x-x^2)*(1-y-y^2)). [U coordinates]