A199334 Triangle T(n,k) = Fibonacci(n+k), related to A000045 (Fibonacci numbers).

0, 1, 1, 1, 2, 3, 2, 3, 5, 8, 3, 5, 8, 13, 21, 5, 8, 13, 21, 34, 55, 8, 13, 21, 34, 55, 89, 144, 13, 21, 34, 55, 89, 144, 233, 377, 21, 34, 55, 89, 144, 233, 377, 610, 987, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584

Offset: 0

Author

Philippe Deléham, Nov 07 2011

Keywords

• easy
• nonn
• tabl

Examples

			Triangle begins :
   0;
   1,  1;
   1,  2,  3;
   2,  3,  5,  8;
   3,  5,  8, 13, 21;
   5,  8, 13, 21, 34,  55;
   8, 13, 21, 34, 55,  89, 144;
  13, 21, 34, 55, 89, 144, 233, 377;
  ...
		

Crossrefs

Cf. A000045, A001906, A014445.

Row sums give A362067.

Formula

T(n,0) = Fibonacci(n) = A000045(n),

T(n,n) = Fibonacci(2n) = A001906(n),

T(2n,n) = Fibonacci(3n) = A014445(n).

T(n,k) = T(n,k-1) + T(n-1,k-1) = T(n-1,k-1) + T(n-1,k).