A061489 Numbers that are Fibonacci numbers plus or minus 1.

0, 1, 2, 3, 4, 6, 7, 9, 12, 14, 20, 22, 33, 35, 54, 56, 88, 90, 143, 145, 232, 234, 376, 378, 609, 611, 986, 988, 1596, 1598, 2583, 2585, 4180, 4182, 6764, 6766, 10945, 10947, 17710, 17712, 28656, 28658, 46367, 46369, 75024, 75026, 121392, 121394, 196417

Offset: 1

Author

N. J. A. Sloane, Nov 08 2001

Keywords

• nonn
• easy

Comments

Only the first four terms are Fibonacci numbers per se. - Alonso del Arte, Oct 05 2017

Links

• Harry J. Smith, Table of n, a(n) for n=1..500
• Ron Knott, The Mathematical Magic of the Fibonacci Numbers.
• Index entries for linear recurrences with constant coefficients, signature (-1,1,1,1,1).

Crossrefs

Cf. A000071, A001611 (the union of those two sequences forms this sequence).

Programs

Mathematica

Union[Table[Fibonacci[i] - 1, {i, 30}], Table[Fibonacci[j] + 1, {j, 0, 30}]]
Union[Flatten[# + {1, -1} &/@ Fibonacci[Range[30]]]] (* Harvey P. Dale, Dec 26 2015 *)

PARI

{ t="b061489.txt"; for (n=1, 4, write(t, n, " ", n - 1) ); g=3; h=2; for (n=3, 250, f=g + h; h=g; g=f; write(t, 2*n - 1, " ", f - 1); write(t, 2*n, " ", f + 1) ) } \\ Harry J. Smith, Jul 23 2009

Formula

a(n) = -a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n+5), for n >= 10. - Amiram Eldar, Jun 24 2023

Extensions

More terms from Robert G. Wilson v, Nov 12 2001