A108037 Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.

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

Offset: 0

Author

N. J. A. Sloane, Jun 01 2005

Keywords

• nonn
• tabl

Examples

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

Links

• Reinhard Zumkeller, Rows n = 0..120 of triangle, flattened

Crossrefs

Cf. A039913, A108036, A108035.

Cf. A099920 (row sums).

Programs

Haskell

a108037 n k = a108037_tabl !! n !! k
a108037_row n = a108037_tabl !! n
a108037_tabl = zipWith replicate [1..] a000045_list
-- Reinhard Zumkeller, Oct 07 2012

Mathematica

Table[Table[Fibonacci[n],{n+1}],{n,0,12}]//Flatten (* Harvey P. Dale, May 07 2017 *)

Python

from math import isqrt
from sympy import fibonacci
def A108037(n): return int(fibonacci((m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)))) # Chai Wah Wu, Nov 07 2024

Formula

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