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A108037
Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
4
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
0,7
LINKS
FORMULA
G.f.: x*(1+y-x*y)/((1-x-x^2)*(1-x*y-x^2*y^2)). [U coordinates]
EXAMPLE
0; 1,1; 1,1,1; 2,2,2,2; 3,3,3,3,3; 5,5,5,5,5,5; ...
MATHEMATICA
Table[Table[Fibonacci[n], {n+1}], {n, 0, 12}]//Flatten (* Harvey P. Dale, May 07 2017 *)
PROG
(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
(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
CROSSREFS
Cf. A099920 (row sums).
Sequence in context: A176146 A171481 A230775 * A237354 A261104 A326032
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 01 2005
STATUS
approved