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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). 12
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 (list; graph; refs; listen; history; text; internal format)
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, 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).

FORMULA

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

a(n) = (7/6)*sqrt(3)*((1+sqrt(3))^n-(1-sqrt(3))^n)+2*((1+sqrt(3))^n+(1-sqrt(3))^n). [Paolo P. Lava, Dec 01 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: A128098 A019495 A019496 * A078141 A090327 A183118

Adjacent sequences:  A021003 A021004 A021005 * A021007 A021008 A021009

KEYWORD

nonn,easy

AUTHOR

R. K. Guy

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.