A199474 Leftmost column in the monotonic justified array of all positive generalized Fibonacci sequences (A160271).

1, 2, 3, 2, 4, 3, 5, 4, 3, 6, 5, 4, 7, 6, 5, 4, 8, 7, 6, 5, 9, 8, 7, 6, 5, 10, 9, 8, 7, 6, 11, 10, 9, 8, 7, 6, 12, 11, 10, 9, 8, 7, 13, 12, 11, 10, 9, 8, 7, 14, 13, 12, 11, 10, 9, 8, 15, 14, 13, 12, 11, 10, 9, 8, 16, 15, 14, 13, 12, 11, 10, 9, 17, 16, 15, 14

Offset

1,2

Comments

Northwest corner of A160271:

1, 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

2, 0, 2, 2, 4, 6, 10, 16, 26, 42, ...

3, 0, 3, 3, 6, 9, 15, 24, 39, 63, ...

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, ...

4, 0, 4, 4, 8, 12, 20, 32, 52, 84, ...

3, 1, 4, 5, 9, 14, 23, 37, 60, 97, ...

5, 0, 5, 5, 10, 15, 25, 40, 65, 105, ...

4, 1, 5, 6, 11, 17, 28, 45, 73, 118, ...

3, 2, 5, 7, 12, 19, 31, 50, 81, 131, ...

...

Links

Table of n, a(n) for n=1..76.

Clark Kimberling, Orderings of the set of all positive Fibonacci sequences, in G. E. Bergum et al., editors, Applications of Fibonacci Numbers, Vol. 5 (1993), pp. 405-416.

Formula

a(n) = (s(n)^2 - n) * [s(n)^2 - s(n) >= n] + (s(n)^2 - n + s(n)) * [s(n)^2 - s(n) < n] where s(n) = ceiling(sqrt(n)). - Iliya Trub, Mar 17 2019

a(n) = A339399(2n). - Wesley Ivan Hurt, Jan 09 2022

a(n) = floor(ceiling(sqrt(4n))^2/4)+floor(sqrt(4n-2))-floor(sqrt(n)+1/2)-n+1. - Wesley Ivan Hurt, Jan 09 2022

Crossrefs

Cf. A160271, A199087, A199088, A339399.

Sequence in context: A264116 A361000 A283368 * A246694 A054384 A026400

Adjacent sequences: A199471 A199472 A199473 * A199475 A199476 A199477

Keyword

nonn

Author

Casey Mongoven, Nov 06 2011

Status

approved