A141169 Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Mar 21 2011

Keywords

• nonn
• tabl

Comments

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

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

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

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

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

Links

• Reinhard Zumkeller, Rows n=0..125 of triangle, flattened

Crossrefs

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

Programs

Haskell

import Data.List (inits)
a141169 n k = a141169_tabl !! n !! k
a141169_row n = a141169_tabl !! n
a141169_tabl = tail $ inits a000045_list
a141169_list = concat $ a141169_tabl
-- Reinhard Zumkeller, Aug 24 2015, Mar 21 2011