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%I #44 Sep 08 2022 08:45:19
%S 1,1,1,1,1,1,2,2,3,3,4,4,6,6,9,9,13,13,19,19,28,28,41,41,60,60,88,88,
%T 129,129,189,189,277,277,406,406,595,595,872,872,1278,1278,1873,1873,
%U 2745,2745,4023,4023,5896,5896,8641,8641,12664,12664,18560,18560
%N Sequence A000930 with terms repeated.
%C The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - _N. J. A. Sloane_
%C Based on the morphism 1->{5}, 2->{6}, 3->{4}, 4->{2}, 5->{3}, 6->{1, 6}.
%H G. C. Greubel, <a href="/A108104/b108104.txt">Table of n, a(n) for n = 0..1000</a>
%H Sergio Falcon, <a href="http://www.geman.in/yahoo_site_admin/assets/docs/13_GMN-5642-V25N2.4320911.pdf">Generalized (k,r)-Fibonacci Numbers</a>, Gen. Math. Notes, 25(2), 2014, 148-158.
%H I. Wloch, U. Bednarz, D. Bród, A Wloch and M. Wolowiec-Musial, <a href="http://dx.doi.org/10.1016/j.dam.2013.05.029">On a new type of distance Fibonacci numbers</a>, Discrete Applied Math., Volume 161, Issues 16-17, November 2013, Pages 2695-2701.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1).
%F a(n) = a(n-2) + a(n-6), starting 1,1,1,1,1,1.
%F G.f.: (1+x)/(1-x^2-x^6).
%t s[1] = {5}; s[2] = {6}; s[3] = {4}; s[4] = {2}; s[5] = {3}; s[6] = {1, 2}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] a0 = Table[Length[p[i]], {i, 0, 50}]
%t m = 6; For[n = 0, n < m, n++, a[n] = 1]; For[n = m, n < 51, n++, a[n] = a[n - m] + a[n - 2]]; Table[a[n], {n, 0, 50}] (* _Sergio Falcon_, Nov 12 2015 *)
%t CoefficientList[Series[(1 + x) / (1 - x^2 - x^6), {x, 0, 50}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1}, 60] (* _Vincenzo Librandi_, Jan 19 2016 *)
%o (PARI) x='x+O('x^55); Vec((1+x)/(1-x^2-x^6)) \\ _Altug Alkan_, Nov 10 2015
%o (Magma) I:=[1,1,1,1,1,1]; [n le 6 select I[n] else Self(n-2)+Self(n-6): n in [1..60]]; // _Vincenzo Librandi_, Jan 19 2016
%Y Cf. A000930.
%K nonn
%O 0,7
%A _Roger L. Bagula_, Jun 03 2005
%E Edited by _N. J. A. Sloane_, Dec 01 2006
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