A372757 8th column of the 3-Zeckendorf array (A136189).

19, 79, 107, 148, 208, 268, 296, 356, 384, 425, 485, 513, 554, 614, 674, 702, 743, 803, 863, 891, 951, 979, 1020, 1080, 1140, 1168, 1228, 1256, 1297, 1357, 1385, 1426, 1486, 1546, 1574, 1634, 1662, 1703, 1763, 1791, 1832, 1892, 1952, 1980, 2021, 2081, 2141

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.
• Jeffrey Shallit, The Narayana Morphism and Related Words, arXiv:2503.01026 [math.CO], 2025.

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), this sequence (k=8).

The k-th prepended column: A005374 (k=1), A136495 (k=2), A023443 (k=3), A202342 (k=4), A372758 (k=5), A372759 (k=6).

Formula

a(n) = 4*A202342(n) + 3*A136496(n) + 6*A381841(n) - 9. - Jeffrey Shallit, Mar 08 2025