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A108104 Sequence A000930 with terms repeated. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

The usual policy in the OEIS is not to include such "doubled" sequences. This is an exception. - N. J. A. Sloane

Based on the morphism 1->{5}, 2->{6}, 3->{4}, 4->{2}, 5->{3}, 6->{1, 6}.

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. BrĂ³d, 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).

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).

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 *)

PROG

(PARI) x='x+O('x^55); Vec((1+x)/(1-x^2-x^6)) \\ Altug Alkan, Nov 10 2015

(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

CROSSREFS

Cf. A000930.

Sequence in context: A210716 A027190 A036824 * A173091 A029025 A035396

Adjacent sequences:  A108101 A108102 A108103 * A108105 A108106 A108107

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Jun 03 2005

EXTENSIONS

Edited by N. J. A. Sloane, Dec 01 2006

STATUS

approved

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Last modified October 17 04:02 EDT 2019. Contains 328106 sequences. (Running on oeis4.)