A372759 6th prepended column of the 3-Zeckendorf array (A136189).

0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23

Offset: 1

Author

A.H.M. Smeets, May 12 2024

Keywords

• nonn

Comments

The 3-Zeckendorf array (A136189) is based on the Narayana (Narayana's cow sequence A000930) weighted representation of n (see A350215).

Links

• Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in k-Zeckendorf arrays, The Fibonacci Quarterly, Vol. 50, No. 1 (February 2012), pp. 11-18.
• Clark Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci Quarterly 33 (1995) 3-8.

Crossrefs

Cf. A000930, A136189, A350215.

The k-th row: A000930(n+2) (k=1), A372760 (k=2).

The k-th column: A020942 (k=1), A064105 (k=2), A064106 (k=3), A372749 (k=4), A372750 (k=5), A372752 (k=6), A372756 (k=7), A372757 (k=8).

The k-th prepended column: A005374 (k=1), A136495 (k=2), A023443 (k=3), A202342 (k=4), A372758 (k=5), this sequence (k=6).

Formula

a(n) = A005374(A372758(n-1)-1) for n >= 3. - Alan Michael Gómez Calderón, Jan 18 2025