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Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.
3

%I #19 Aug 24 2015 02:02:10

%S 0,0,1,0,1,1,0,1,1,2,0,1,1,2,3,0,1,1,2,3,5,0,1,1,2,3,5,8,0,1,1,2,3,5,

%T 8,13,0,1,1,2,3,5,8,13,21,0,1,1,2,3,5,8,13,21,34,0,1,1,2,3,5,8,13,21,

%U 34,55,0,1,1,2,3,5,8,13,21,34,55,89,0,1,1,2,3,5,8,13,21,34,55,89,144,0,1,1,2,3,5,8,13,21

%N Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.

%C T(n,0) = A000004(n); T(n,n) = A000045(n);

%C central terms: T(2*n,n) = A000045(n);

%C sums of rows: Sum(T(n,k): 0<=k<=n) = A000071(n+2);

%C alternating sums of rows: Sum(T(n,k)*(-1)^k: 0<=k<=n) = A119282(n);

%C T(n,k) + T(n,n-k) = A094570(n,k).

%H Reinhard Zumkeller, <a href="/A141169/b141169.txt">Rows n=0..125 of triangle, flattened</a>

%o (Haskell)

%o import Data.List (inits)

%o a141169 n k = a141169_tabl !! n !! k

%o a141169_row n = a141169_tabl !! n

%o a141169_tabl = tail $ inits a000045_list

%o a141169_list = concat $ a141169_tabl

%o -- _Reinhard Zumkeller_, Aug 24 2015, Mar 21 2011

%Y Cf. A000045, A000004, A000071, A094570, A119282.

%K nonn,tabl

%O 0,10

%A _Reinhard Zumkeller_, Mar 21 2011