Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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