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A098150 a(n) = 2(a(n-2) - a(n-1)) + a(n-3) where a(0)=-3, a(1)=11 & a(2)=-30. 3
-3, 11, -30, 79, -207, 542, -1419, 3715, -9726, 25463, -66663, 174526, -456915, 1196219, -3131742, 8199007, -21465279, 56196830, -147125211, 385178803, -1008411198, 2640054791, -6911753175, 18095204734, -47373861027, 124026378347, -324705274014, 850089443695, -2225563057071, 5826599727518, -15254236125483 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Sequence relates bisections of Lucas and Fibonacci numbers.

Pisano period lengths: 1, 3, 4, 6, 5, 12, 8, 6, 12, 15, 10, 12, 7, 24, 20, 12, 9, 12, 18, 30, ... - R. J. Mathar, Aug 10 2012

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..2383

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (-3,-1).

FORMULA

2*A098149(n) + a(n) = 8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1).

a(n) = - 3a(n-1) - a(n-2). - Tanya Khovanova, Feb 02 2007

G.f.: (2x-3)/(1+3x+x^2). - Philippe Deléham, Nov 16 2008

a(n) = -(3/2)*((-3/2)-(1/2)*sqrt(5))^n - (13/10)*((-3/2)-(1/2)*sqrt(5))^n*sqrt(5) + (13/10)*((-3/2)+(1/2)*sqrt(5))^n*sqrt(5) - (3/2)*((-3/2)+(1/2)*sqrt(5))^n, with n>=0. - Paolo P. Lava, Nov 19 2008

MATHEMATICA

a[0] = -3; a[1] = 11; a[2] = -30; a[n_] := a[n] = 2(a[n - 2] - a[n - 1]) + a[n - 3]; Table[ a[n], {n, 0, 25}] (* Robert G. Wilson v, Sep 04 2004 *)

RecurrenceTable[{a[0]==-3, a[1]==11, a[2]==-30, a[n]==2(a[n-2]-a[n-1])+ a[n-3]}, a, {n, 30}] (* or *) LinearRecurrence[{-3, -1}, {-3, 11}, 30] (* Harvey P. Dale, Feb 05 2012 *)

CROSSREFS

Cf. A098149, A001519, A005248.

Sequence in context: A165893 A106397 A167375 * A085376 A196233 A009131

Adjacent sequences:  A098147 A098148 A098149 * A098151 A098152 A098153

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Aug 29 2004

EXTENSIONS

More terms from Robert G. Wilson v, Sep 04 2004

STATUS

approved

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Last modified April 25 08:38 EDT 2017. Contains 285348 sequences.