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
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)
Programs
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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
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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).
Comments