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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

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, 1204139 (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 entries for 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) for all n in Z.

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

G.f. = 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) = my(k = n\3); (-1)^k * if( n%3 == 0, fibonacci( k )^2, 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: A178233 A271356 A201411 * A082051 A196848 A266699

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 | 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 December 8 09:03 EST 2016. Contains 278906 sequences.