A171730 Triangle of differences of Fibonacci numbers.

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

Offset

1,2

Comments

The numbers missing from this triangle form A050939.

Reversing the rows gives A171729.

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

Example

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

Maple

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A050939, A143061, A171729.

Sequence in context: A280514 A246105 A211980 * A131243 A038497 A091355

Adjacent sequences: A171727 A171728 A171729 * A171731 A171732 A171733

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 16 2009

Status

approved