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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A085695 a(n) = Fibonacci(n)*Fibonacci(3n)/2. 2
0, 1, 4, 34, 216, 1525, 10336, 71149, 486864, 3339106, 22881100, 156843721, 1074985344, 7368157369, 50501844796, 346145466850, 2372514562656, 16261461342589, 111457702083424, 763942486626661, 5236139616899400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This is a divisibility sequence, that is, if n | m then a(n) | a(m). However, it is not a strong divisibility sequence. It is the case k = -3 of a 1-parameter family of 4th-order linear divisibility sequences with o.g.f. x*(1 - x^2)/( (1 - k*x + x^2)*(1 - (k^2 - 2)*x + x^2) ). Compare with A000290 (case k = 2) and A215465 (case k = 3). - Peter Bala, Jan 17 2014

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..1197

H. C. Williams and R. K. Guy, Some fourth-order linear divisibility sequences, Intl. J. Number Theory 7 (5) (2011) 1255-1277.

FORMULA

G.f.: ( x - x^3 )/( 1 - 4 x - 19 x^2 - 4 x^3 + x^4 ) Recurrence: a(n+4) = 4 a(n+3) + 19 a(n+2) + 4 a(n+1) - a(n)

MATHEMATICA

Array[Times @@ MapIndexed[Fibonacci[#]/First@ #2 &, {#, 3 #}] &, 21, 0] (* or *) LinearRecurrence[{4, 19, 4, -1}, {0, 1, 4, 34}, 21] (* or *)

CoefficientList[Series[(x - x^3)/(1 - 4 x - 19 x^2 - 4 x^3 + x^4), {x, 0, 20}], x] (* Michael De Vlieger, Dec 17 2017 *)

PROG

(MuPAD) numlib::fibonacci(3*n)*numlib::fibonacci(n)/2 $ n = 0..35; // Zerinvary Lajos, May 13 2008

(PARI) a(n) = fibonacci(n)*fibonacci(3*n)/2 \\ Andrew Howroyd, Dec 17 2017

CROSSREFS

Cf. A215465.

Sequence in context: A231518 A196908 A197075 * A049293 A198687 A116430

Adjacent sequences:  A085692 A085693 A085694 * A085696 A085697 A085698

KEYWORD

easy,nonn

AUTHOR

Emanuele Munarini, Jul 18 2003

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 24 05:06 EDT 2019. Contains 325290 sequences. (Running on oeis4.)