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2nd row of the 3-Zeckendorf array (A136189), including prepended terms.
5

%I #14 May 25 2024 14:52:56

%S 0,2,1,1,3,4,5,8,12,17,25,37,54,79,116,170,249,365,535,784,1149,1684,

%T 2468,3617,5301,7769,11386,16687,24456,35842,52529,76985,112827,

%U 165356,242341,355168,520524,762865,1118033,1638557,2401422,3519455,5158012,7559434

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

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

%H Paolo Xausa, <a href="/A372760/b372760.txt">Table of n, a(n) for n = -5..1000</a>

%H Larry Ericksen and Peter G. Anderson, <a href="https://www.fq.math.ca/Papers1/50-1/EricksenAnderson.pdf">Patterns in differences between rows in k-Zeckendorf arrays</a>, The Fibonacci Quarterly, Vol. 50, No. 1 (February 2012), pp. 11-18.

%H Clark Kimberling, <a href="http://www.fq.math.ca/Scanned/33-1/kimberling.pdf">The Zeckendorf array equals the Wythoff array</a>, Fibonacci Quarterly 33 (1995) 3-8.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1).

%F a(n) = A179070(n+5) for n >= -3. - _Pontus von Brömssen_, May 13 2024

%t LinearRecurrence[{1, 0, 1}, {0, 2, 1}, 50] (* _Paolo Xausa_, May 25 2024 *)

%Y Cf. A000930, A136189, A179070, A350215.

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

%Y 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).

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

%K nonn,easy

%O -5,2

%A _A.H.M. Smeets_, May 12 2024