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!)
A018910 Pisot sequence L(4,5). 10
4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157, 165580143 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993

Index entries for linear recurrences with constant coefficients, signature (2, 0, -1).

Index entries for Pisot sequences

FORMULA

a(n) = Fib(n+3)+2 = A020743(n-2) = A157725(n+3); a(n) = 2a(n-1) - a(n-3).

G.f.: -(-4+3*x+3*x^2)/(x-1)/(x^2+x-1) = -2/(x-1)+(-x-2)/(x^2+x-1) . - R. J. Mathar, Nov 23 2007

a(n)=2+((5+2r5)/5)((1+r5)/2)^n+((5-2r5)/5)((1-r5)/2)^n, where r5 = sqrt(5).

- Paolo P. Lava, Jun 10 2008

MATHEMATICA

LinearRecurrence[{2, 0, -1}, {4, 5, 7}, 40] (* Jean-Fran├žois Alcover, Dec 12 2016 *)

PROG

(PARI) pisotL(nmax, a1, a2) = {

  a=vector(nmax); a[1]=a1; a[2]=a2;

  for(n=3, nmax, a[n] = ceil(a[n-1]^2/a[n-2]));

  a

}

pisotL(50, 4, 5) \\ Colin Barker, Aug 07 2016

CROSSREFS

See A008776 for definitions of Pisot sequences.

Sequence in context: A093517 A248858 A145018 * A022936 A057708 A032686

Adjacent sequences:  A018907 A018908 A018909 * A018911 A018912 A018913

KEYWORD

nonn,easy

AUTHOR

R. K. Guy

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 27 15:22 EDT 2017. Contains 287207 sequences.