A094570 - OEIS

%I #22 Mar 22 2021 06:28:13

%S 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 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 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 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 Reinhard Zumkeller, <a href="/A094570/b094570.txt">Rows n=0..125 of triangle, flattened</a>

%F 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 From _Reinhard Zumkeller_, Mar 21 2011: (Start)

%F T(n,0) = T(n,n) = A000045(n).

%F T(2*n,n) = A006355(n+1).

%F T(n,k) = A141169(n,k) + A141169(n,n-k). (End)

%F Sum(T(n,k), 0<=k<=n) = 2*A000071(n+2) = 2*A000045(n+2) - 2. - _Philippe Deléham_, Apr 07 2013

%e Triangle begins:

%e 0;

%e 1, 1;

%e 1, 2, 1;

%e 2, 2, 2, 2;

%e 3, 3, 2, 3, 3;

%e 5, 4, 3, 3, 4, 5;

%e 8, 6, 4, 4, 4, 6, 8;

%e 13, 9, 6, 5, 5, 6, 9, 13;

%e 21, 14, 9, 7, 6, 7, 9, 14, 21;

%o (PARI) row(n) = vector(n+1, k, k--; fibonacci(k)+fibonacci(n-k)); \\ _Michel Marcus_, Mar 22 2021

%Y Cf. A000045, A000071, A006355, A141169.

%K nonn,tabl

%O 0,5

%A _Clark Kimberling_, May 12 2004