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

%I A108037 #13 Nov 07 2024 20:40:16
%S A108037 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,
%T A108037 13,13,13,13,21,21,21,21,21,21,21,21,21,34,34,34,34,34,34,34,34,34,34,
%U A108037 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
%N A108037 Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
%H A108037 Reinhard Zumkeller, <a href="/A108037/b108037.txt">Rows n = 0..120 of triangle, flattened</a>
%F A108037 G.f.: x*(1+y-x*y)/((1-x-x^2)*(1-x*y-x^2*y^2)). [U coordinates]
%e A108037 0; 1,1; 1,1,1; 2,2,2,2; 3,3,3,3,3; 5,5,5,5,5,5; ...
%t A108037 Table[Table[Fibonacci[n],{n+1}],{n,0,12}]//Flatten (* _Harvey P. Dale_, May 07 2017 *)
%o A108037 (Haskell)
%o A108037 a108037 n k = a108037_tabl !! n !! k
%o A108037 a108037_row n = a108037_tabl !! n
%o A108037 a108037_tabl = zipWith replicate [1..] a000045_list
%o A108037 -- _Reinhard Zumkeller_, Oct 07 2012
%o A108037 (Python)
%o A108037 from math import isqrt
%o A108037 from sympy import fibonacci
%o A108037 def A108037(n): return int(fibonacci((m:=isqrt(k:=n+1<<1))-(k<=m*(m+1)))) # _Chai Wah Wu_, Nov 07 2024
%Y A108037 Cf. A039913, A108036, A108035.
%Y A108037 Cf. A099920 (row sums).
%K A108037 nonn,tabl
%O A108037 0,7
%A A108037 _N. J. A. Sloane_, Jun 01 2005