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

1,2

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

Cf. A000045, A039913, A108036, A108037.

Cf. A023607 (row sums).

Sequence in context: A295629 A076272 A180101 * A202503 A049747 A260684

Adjacent sequences: A108032 A108033 A108034 * A108036 A108037 A108038

Keyword

nonn,tabl

Author

N. J. A. Sloane, Jun 01 2005

Extensions

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

Status

approved