A108104 Sequence A000930 with terms repeated.
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, 129, 129, 189, 189, 277, 277, 406, 406, 595, 595, 872, 872, 1278, 1278, 1873, 1873, 2745, 2745, 4023, 4023, 5896, 5896, 8641, 8641, 12664, 12664, 18560, 18560
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Sergio Falcon, Generalized (k,r)-Fibonacci Numbers, Gen. Math. Notes, 25(2), 2014, 148-158.
- I. Wloch, U. Bednarz, D. Bród, A Wloch and M. Wolowiec-Musial, On a new type of distance Fibonacci numbers, Discrete Applied Math., Volume 161, Issues 16-17, November 2013, Pages 2695-2701.
- Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1).
Crossrefs
Cf. A000930.
Programs
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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
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Mathematica
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}] 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 *) 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 *) -
PARI
x='x+O('x^55); Vec((1+x)/(1-x^2-x^6)) \\ Altug Alkan, Nov 10 2015
Formula
a(n) = a(n-2) + a(n-6), starting 1,1,1,1,1,1.
G.f.: (1+x)/(1-x^2-x^6).
Extensions
Edited by N. J. A. Sloane, Dec 01 2006
Comments