A171729 Triangle of differences of Fibonacci numbers, rows ascending.

1, 1, 2, 1, 2, 3, 2, 3, 4, 5, 3, 5, 6, 7, 8, 5, 8, 10, 11, 12, 13, 8, 13, 16, 18, 19, 20, 21, 13, 21, 26, 29, 31, 32, 33, 34, 21, 34, 42, 47, 50, 52, 53, 54, 55, 34, 55, 68, 76, 81, 84, 86, 87, 88, 89, 55, 89, 110, 123, 131, 136, 139, 141, 142, 143, 144, 89, 144, 178, 199, 212, 220, 225, 228, 230, 231, 232, 233

Offset: 1

Author

Clark Kimberling, Dec 16 2009

Keywords

• nonn
• tabl

Comments

The numbers missing from this triangle form A050939.

Row n of this triangle has one more term than row n of A143061.

Reversing the rows gives A171730.

Examples

			First rows:
  1
  1 2
  1 2  3
  2 3  4  5
  3 5  6  7  8
  5 8 10 11 12 13
  ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows n = 1..150, flattened)

Crossrefs

Cf. A000045, A050939, A143061, A171730.

Programs

Maple

F:= combinat[fibonacci]:
T:= (n,k)-> F(n+1)-`if`(k=n, 0, F(n-k+1)):
seq(seq(T(n,k), k=1..n), n=1..12);  # Alois P. Heinz, Feb 06 2023

Mathematica

Table[Fibonacci[n + 1] - If[k < n, Fibonacci[n - k + 1], 0], {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Feb 06 2023 *)

PARI

row(n) = vector(n, k, fibonacci(n+1) - if (kMichel Marcus, Feb 06 2023

Formula

Counting the top row as the first row, the n-th row is

F(n+1)-F(n), F(n+1)-F(n-1), ..., F(n+1)-F(2), F(n+1)-F(0).