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

1,3

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.

Links

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

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).

Example

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

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 *)

Prog

(PARI) row(n) = vector(n, k, fibonacci(n+1) - if (k<n, fibonacci(n-k+1), 0)); \\ Michel Marcus, Feb 06 2023

Crossrefs

Cf. A000045, A050939, A143061, A171730.

Sequence in context: A211990 A162618 A036576 * A356999 A127255 A174832

Adjacent sequences: A171726 A171727 A171728 * A171730 A171731 A171732

Keyword

nonn,tabl,changed

Author

Clark Kimberling, Dec 16 2009

Status

approved