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

Author

Casey Mongoven, Nov 06 2011

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A160271, A199087, A199088, A339399.

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