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

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A206282 a(n) = ( a(n-1) * a(n-3) + a(n-2) ) / a(n-4), a(1) = a(2) = 1, a(3) = -1, a(4) = -4. 1
1, 1, -1, -4, -5, 1, 9, 11, -4, -25, -31, 9, 64, 79, -25, -169, -209, 64, 441, 545, -169, -1156, -1429, 441, 3025, 3739, -1156, -7921, -9791, 3025, 20736, 25631, -7921, -54289, -67105, 20736, 142129, 175681, -54289, -372100, -459941, 142129, 974169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This satisfies the same recurrence as Dana Scott's sequence A048736.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..5000

Index to sequences with linear recurrences with constant coefficients, signature (0,0,-2,0,0,2,0,0,1).

FORMULA

G.f.: x * (1 + x - x^2 - 2*x^3 - 3*x^4 - x^5 - x^6 - x^7) / (1 + 2*x^3 - 2*x^6 - x^9).

a(-5 - n) = a(n) = a(n+2) * a(n-2) - a(n+1) * a(n-1).

a(3*n) = (-1)^n * F(n)^2, a(3*n + 1) = (-1)^n * F(n + 2)^2 where F = Fibonacci A000045.

a(6*n - 4) = - A110034(2*n), a(6*n - 1) = - A110035(2*n), a(3*n + 2) = (-1)^n * A126116(2*n + 3).

EXAMPLE

x + x^2 - x^3 - 4*x^4 - 5*x^5 + x^6 + 9*x^7 + 11*x^8 - 4*x^9 - 25*x^10 + ...

PROG

(PARI) {a(n) = local(k = n\3); (-1)^k * if( n%3 == 0, fibonacci( k )^2, if (n%3 == 1, fibonacci( k+2 )^2, fibonacci( k ) * fibonacci( k+3 ) + fibonacci( k+1 ) * fibonacci( k+2 )))}

(Haskell)

a206282 n = a206282_list !! (n-1)

a206282_list = 1 : 1 : -1 : -4 :

   zipWith div

     (zipWith (+)

       (zipWith (*) (drop 3 a206282_list)

                    (drop 1 a206282_list))

       (drop 2 a206282_list))

     a206282_list

-- Same program as in A048736, see comment.

-- Reinhard Zumkeller, Feb 08 2012

CROSSREFS

Cf. A000045, A048736, A110034, A110035, A126116.

Sequence in context: A199384 A178233 A201411 * A082051 A196848 A234937

Adjacent sequences:  A206279 A206280 A206281 * A206283 A206284 A206285

KEYWORD

sign,easy

AUTHOR

Michael Somos, Feb 05 2012

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified December 21 19:36 EST 2014. Contains 252325 sequences.