A108035 Triangle read by rows: n-th row consists of n copies of the n-th nonzero Fibonacci number.

1, 2, 2, 3, 3, 3, 5, 5, 5, 5, 8, 8, 8, 8, 8, 13, 13, 13, 13, 13, 13, 21, 21, 21, 21, 21, 21, 21, 34, 34, 34, 34, 34, 34, 34, 34, 55, 55, 55, 55, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 89, 89, 89, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233

Offset: 1

Author

N. J. A. Sloane, Jun 01 2005

Keywords

• nonn
• tabl

Examples

			1; 2,2; 3,3,3; 5,5,5,5; 8,8,8,8,8; ...
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

Crossrefs

Cf. A000045, A039913, A108036, A108037.

Cf. A023607 (row sums).

Programs

Haskell

a108035 n k = a108035_tabl !! (n-1) !! (n-1)
a108035_row n = a108035_tabl !! (n-1)
a108035_tabl = zipWith replicate [1..] $ drop 2 a000045_list
-- Reinhard Zumkeller, Oct 07 2012

Mathematica

Flatten[Table[Table[Fibonacci[n],{n-1}],{n,13}]] (* Harvey P. Dale, Jul 18 2015 *)

Python

from math import isqrt
from sympy import fibonacci
def A108035(n): return int(fibonacci(1+(m:=isqrt(k:=n<<1))+(k>m*(m+1)))) # Chai Wah Wu, Nov 07 2024

Formula

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

Extensions

Definition clarified by N. J. A. Sloane, Nov 09 2024