A021006 Pisot sequence P(4,11), a(0)=4, a(1)=11, a(n+1) is the nearest integer to a(n)^2/a(n-1). Evidently satisfies a(n) = 2*a(n-1)+2*a(n-2).

4, 11, 30, 82, 224, 612, 1672, 4568, 12480, 34096, 93152, 254496, 695296, 1899584, 5189760, 14178688, 38736896, 105831168, 289136128, 789934592, 2158141440, 5896152064, 16108587008, 44009478144, 120236130304

Offset

0,1

Comments

Pisano period lengths: 1, 1, 3, 1, 24, 3, 48, 1, 9, 24, 10, 3, 12, 48, 24, 1,144, 9,180, 24,,.. - R. J. Mathar, Aug 10 2012

Inverse binomial transform of A001353 without its first two terms, and downshift. - Richard R. Forberg, Aug 24 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Tanya Khovanova, Recursive Sequences

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

Index entries for Pisot sequences

Formula

G.f.: (4+3*x)/(1-2*x-2*x^2). [Philippe Deléham, Nov 19 2008]

Mathematica

LinearRecurrence[{2, 2}, {4, 11}, 30] (* Harvey P. Dale, Oct 25 2011 *)

Prog

(Magma) I:=[4, 11]; [n le 2 select I[n] else 2*Self(n-1)+2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 26 2011

Crossrefs

Sequence in context: A341104 A019495 A019496 * A078141 A090327 A183118

Adjacent sequences: A021003 A021004 A021005 * A021007 A021008 A021009

Keyword

nonn,easy

Author

R. K. Guy

Status

approved