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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127595 a(n)=F(4n)-2F(2n) where F(n)= Fibonacci numbers A000045. 4
0, 1, 15, 128, 945, 6655, 46080, 317057, 2176335, 14925184, 102320625, 701373311, 4807434240, 32951037313, 225850798095, 1548007091840, 10610205501105, 72723448842367, 498453982018560, 3416454544730369, 23416728143799375 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is a divisibility sequence; that is, if h|k then a(h)|a(k).

LINKS

Table of n, a(n) for n=0..20.

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

H. C. Williams and R. K. Guy, Odd and even linear divisibility sequences of order 4, INTEGERS, 2015, #A33.

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (10,-23,10,-1).

FORMULA

a(n) = F(2n)*(L(2n)-2) = A001906(n)*A004146(n), where L(n) are the Lucas numbers A000032.

a(2n) = 5*(F(2n))^3*L(2n), a(2n+1) = F(2n+1)*L(2n+1)^3.

a(n) = [(Phi^(2n))-1]^2*[(Phi^(4n))-1]/[sqrt(5)*(Phi^(4n))].

G.f.: A(x)=x*(1+(r+2)*x+x^2)/((1-r*x+x^2)*(1-(r^2-2)*x+x^2)) at r=3. The case r=2 is A000578.

CROSSREFS

Cf. A000032, A000045, A001906, A004146.

Sequence in context: A198850 A283120 A209404 * A056579 A294054 A156922

Adjacent sequences:  A127592 A127593 A127594 * A127596 A127597 A127598

KEYWORD

easy,nonn

AUTHOR

Peter Bala, Apr 10 2007

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 November 13 23:01 EST 2019. Contains 329106 sequences. (Running on oeis4.)