login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A014437 Odd Fibonacci numbers. 10
1, 1, 3, 5, 13, 21, 55, 89, 233, 377, 987, 1597, 4181, 6765, 17711, 28657, 75025, 121393, 317811, 514229, 1346269, 2178309, 5702887, 9227465, 24157817, 39088169, 102334155, 165580141, 433494437, 701408733, 1836311903, 2971215073 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Starting with offset 1 = row sums of triangle A177995. - Gary W. Adamson, May 16 2010

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (0,4,0,1).

FORMULA

Fibonacci(3n+1) union Fibonacci(3n+2).

a(n) = Fibonacci(3*floor((n+1)/2)) + (-1)^n). - Antti Karttunen, Feb 05 2001

G.f.: ( -1-x+x^2-x^3 ) / ( -1+4*x^2+x^4 ). - R. J. Mathar, Feb 16 2011

a(2n) = v-w, a(2n+1) = v+w, with v=A001076(n+1), w=A001076(n). Therefore, a(2n)+a(2n+1) = 2*A001076(n+1). - Ralf Stephan, Aug 31 2013

From Vladimir Reshetnikov, Oct 30 2015: (Start)

a(n) = ((cos(Pi*n/2)-sqrt(phi)*sin(Pi*n/2))/phi^((3*n+2)/2) + (sqrt(phi)*cos(Pi*n/2)^2+sin(Pi*n/2)^2)*phi^((3*n+1)/2))/sqrt(5), where phi=(1+sqrt(5))/2.

E.g.f.: (cos(x/phi^(3/2))/phi - sin(x/phi^(3/2))/sqrt(phi) + cosh(x*phi^(3/2))*phi + sinh(x*phi^(3/2))*sqrt(phi))/sqrt(5).

(End)

MAPLE

with(combinat):A014437:=proc(n)return fibonacci((3*floor((n+1)/2)) + (-1)^n):end:

seq(A014437(n), n=0..31); # Nathaniel Johnston, Apr 18 2011

MATHEMATICA

a={}; Do[f=Fibonacci[n]; If[OddQ[f], AppendTo[a, f]], {n, 1, 30, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)

RecurrenceTable[{a[n] == 4*a[n-2] + a[n-4], a[0]==1, a[1]==1, a[2]==3, a[3]==5, }, a, {n, 0, 500}] (* G. C. Greubel, Oct 30 2015 *)

PROG

(MAGMA) [Fibonacci((3*Floor((n+1)/2)) + (-1)^n): n in [0..50]]; // Vincenzo Librandi, Apr 18 2011

(PARI) Vec((-1-x+x^2-x^3)/(-1+4*x^2+x^4) + O(x^200)) \\ Altug Alkan, Oct 31 2015

CROSSREFS

Cf. A001651, A059878, A000045.

Cf. A177995. - Gary W. Adamson, May 16 2010

Sequence in context: A283752 A283602 A283817 * A153866 A104222 A240070

Adjacent sequences:  A014434 A014435 A014436 * A014438 A014439 A014440

KEYWORD

nonn,easy

AUTHOR

Mohammad K. Azarian

EXTENSIONS

a(30)-a(31) from Vincenzo Librandi, Apr 18 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 28 16:24 EDT 2017. Contains 287241 sequences.