A372760 2nd row of the 3-Zeckendorf array (A136189), including prepended terms.

0, 2, 1, 1, 3, 4, 5, 8, 12, 17, 25, 37, 54, 79, 116, 170, 249, 365, 535, 784, 1149, 1684, 2468, 3617, 5301, 7769, 11386, 16687, 24456, 35842, 52529, 76985, 112827, 165356, 242341, 355168, 520524, 762865, 1118033, 1638557, 2401422, 3519455, 5158012, 7559434

Offset

-5,2

Comments

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

Links

Paolo Xausa, Table of n, a(n) for n = -5..1000

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.

Index entries for linear recurrences with constant coefficients, signature (1,0,1).

Formula

a(n) = A179070(n+5) for n >= -3. - Pontus von Brömssen, May 13 2024

Mathematica

LinearRecurrence[{1, 0, 1}, {0, 2, 1}, 50] (* Paolo Xausa, May 25 2024 *)

Crossrefs

Cf. A000930, A136189, A179070, A350215.

The k-th row: A000930(n+2) (k=1), this sequence (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), A372759 (k=6).

Sequence in context: A278028 A124424 A057044 * A153899 A068098 A135722

Adjacent sequences: A372757 A372758 A372759 * A372761 A372762 A372763

Keyword

nonn,easy

Author

A.H.M. Smeets, May 12 2024

Status

approved