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A094570 Triangle T(n,k) read by rows: T(n,k) = F(k) + F(n-k) where F(n) is the n-th Fibonacci number.

%I A094570 #22 Mar 22 2021 06:28:13
%S A094570 0,1,1,1,2,1,2,2,2,2,3,3,2,3,3,5,4,3,3,4,5,8,6,4,4,4,6,8,13,9,6,5,5,6,
%T A094570 9,13,21,14,9,7,6,7,9,14,21,34,22,14,10,8,8,10,14,22,34,55,35,22,15,
%U A094570 11,10,11,15,22,35,55,89,56,35,23,16,13,13,16,23,35,56,89,144,90,56,36,24,18,16,18,24,36,56,90,144
%N A094570 Triangle T(n,k) read by rows: T(n,k) = F(k) + F(n-k) where F(n) is the n-th Fibonacci number.
%H A094570 Reinhard Zumkeller, <a href="/A094570/b094570.txt">Rows n=0..125 of triangle, flattened</a>
%F A094570 Row n: F(0)+F(n), F(1)+F(n-1), F(2)+F(n-2), ..., F(n-1)+F(1), F(n)+F(0).
%F A094570 From _Reinhard Zumkeller_, Mar 21 2011: (Start)
%F A094570 T(n,0) = T(n,n) = A000045(n).
%F A094570 T(2*n,n) = A006355(n+1).
%F A094570 T(n,k) = A141169(n,k) + A141169(n,n-k). (End)
%F A094570 Sum(T(n,k), 0<=k<=n) = 2*A000071(n+2) = 2*A000045(n+2) - 2. - _Philippe Deléham_, Apr 07 2013
%e A094570 Triangle begins:
%e A094570 0;
%e A094570 1, 1;
%e A094570 1, 2, 1;
%e A094570 2, 2, 2, 2;
%e A094570 3, 3, 2, 3, 3;
%e A094570 5, 4, 3, 3, 4, 5;
%e A094570 8, 6, 4, 4, 4, 6, 8;
%e A094570 13, 9, 6, 5, 5, 6, 9, 13;
%e A094570 21, 14, 9, 7, 6, 7, 9, 14, 21;
%o A094570 (PARI) row(n) = vector(n+1, k, k--; fibonacci(k)+fibonacci(n-k)); \\ _Michel Marcus_, Mar 22 2021
%Y A094570 Cf. A000045, A000071, A006355, A141169.
%K A094570 nonn,tabl
%O A094570 0,5
%A A094570 _Clark Kimberling_, May 12 2004