A171730 Triangle of differences of Fibonacci numbers, rows descending.

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

Author

Clark Kimberling, Dec 16 2009

Keywords

• nonn
• tabl

Comments

The numbers missing from this triangle form A050939.

Reversing the rows gives A171729.

Examples

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

Links

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

Crossrefs

Cf. A000045, A050939, A143061, A171729.

Programs

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 *)

PARI

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

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).