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

1,1

Comments

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

Links

Table of n, a(n) for n=1..47.

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.

Formula

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

Sequence in context: A041700 A213832 A350194 * A132234 A074822 A139871

Adjacent sequences: A372754 A372755 A372756 * A372758 A372759 A372760

Keyword

nonn,changed

Author

A.H.M. Smeets, May 12 2024

Status

approved