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A105426 a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2). 3
1, 5, 39, 307, 2417, 19029, 149815, 1179491, 9286113, 73109413, 575589191, 4531604115, 35677243729, 280886345717, 2211413522007, 17410421830339, 137071961120705, 1079165267135301, 8496250175961703, 66890836140558323 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

15*a(n)^2-14 is a square for all n.

LINKS

Table of n, a(n) for n=0..19.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (8,-1).

Index entries for two-way infinite sequences

FORMULA

G.f.: (1-3x)/(1-8x+x^2). a(n)=2*A105045(2*n+1)-1. a(-n)=2*A105045(2*n)-1, if n>0.

a(n)=(1/2)*[4-sqrt(15)]^n-(1/30)*[4-sqrt(15)]^n*sqrt(15)+(1/2)*[4+sqrt(15)]^n+(1/30)*sqrt(15) *[4+sqrt(15)]^n, with n>=0 - Paolo P. Lava, Jul 08 2008

MATHEMATICA

LinearRecurrence[{8, -1}, {1, 5}, 20] (* Harvey P. Dale, Feb 25 2016 *)

PROG

(PARI) a(n)=subst(19*poltchebi(n)-poltchebi(n-1), x, 4)/15

CROSSREFS

Cf. a(n) = A001090(n+1) - 3*A001090(n).

Sequence in context: A221357 A201442 A135849 * A273019 A244039 A213233

Adjacent sequences:  A105423 A105424 A105425 * A105427 A105428 A105429

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Apr 10 2005

STATUS

approved

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Last modified May 29 11:23 EDT 2017. Contains 287246 sequences.